basic physic report pendulum (fix)

8/16/2019 Basic Physic Report PENDULUM (Fix)

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Pendulum

Sitrah Nurdini Irwan*, A.Lisra Andriani Hasrat, Helny Lydarisbo, Nurul Angelita

Basic Physic Laboratory of FMIPA

State University of Makassar 20!

Abstract" Has done experiment about pendulum mathematical, pendulum mathematical is anobject that was hanging in a lightweight rope hae length remains, and i! objects gien a bywaywith an angle "#$ and released objects will then swinging on the ertical plane because style⁰heay in!luence. %his experiment conducted with purpose& 'an understand !actors in!luencing the period oscilation mathematical pendulum, determine the acceleration o! graity with the simple

oscilation, can determine the alue o! the period oscilation pendulum(! an experiment that has been carried out, seen !rom the results o! direct obseration that what is

meant by the period is a time lapse re)uired by an object to do one complete ibration.ibration isthe gesture o! the bac+ and !orth o! which there are around any point balance in which thewea+ness o! the strong in!luenced the sie o! energy gien. (ne ibration !re)uency is once !ull o! motion bac+ and !orth. (ne complete ibration is moement !rom point A and bac+ at A point, and

continues to be long rope that is used the more slow motion pendulum is moing, and the shorter arope pendulum used the more )uic+ly pendulum is moing#ey$ords& -eiation, ass, (scilation, /endulum, /eriod

F%&MULA'I%( %F ')* P&%BL*M

#. 0hat is !actors that in!luence at all on the period oscilation mathematical

pendulum1

2. How to determine the acceleration o! graity with the methods oscilation simple1

3. How to determine the alue o! the period oscilation mathematical pendulum1

PU&P%S*

#. 4nderstand !actors in!luencing the period oscilation mathematical pendulum

2. -etermine the acceleration o! graity with the simple oscilation

3. 'an determine the alue o! the period oscilation pendulum

B&I*F ')*%&+

Heay is graitational !orces against objects. %he acceleration o! graity 5g6 was

acceleration o! experienced by objects under its own weight. According to -alton7s law II

style 8 9 m.a repeat this style heay objects 8 9 m.g . :urden !astened at the end o! a

rope light whose mass is can be neglected called pendulum. /endulum mathematical is

one o! mathematical who moing to motion harmonic simple athematical pendulum is

the ideal consisting o! a point mass was hanging on a lightweight rope not mass. I!

pendulum is deiated with the corner ϑ !rom a position setimbangnya and released the

pendulum will swinging in the ertical plane because o! the graity. %he principle o!

oscilation i! the an object that was hanging in a rope, gien a byway, and released, it will

swinging to the right and to the le!t. eaning!ul when bodies are on the le!t will be

accelerated to right, and when objects hae at right so will be slowed and stop, and

accelerated le!t and so on


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(! this moement seen that objects accelerated along its motions. According to Newton7s

law 58 9 m.a6 Accelerated only arises when there is style. %he direction o! the

acceleration and the direction o! the !orce always the same.

/icture #. Ilustration o! mathematical pendulum0hen the weight hanging in swing and not gien style so objects will dwell in a point

e)uilibrium :. I! the drawn to point a and released, so burden will moe into :, ', and

bac+ to A. %he moement o! the load will happen recurring periodically, in other words a

load on swing aboe to compare motion harmonic simple. (n aboe example, things

begin to moe !rom point A and to point :, the ' and bac+ again to : and A.%he

se)uence is A;:;';:;A. I! objects released !rom the point ' so the order his moement is

';:;A;:;'. I! the drawn one side, then released hence a burden will swinging !rom the

balance toward the other hand. I! amplitude swing small, it is that simple and pendulum

will conducted ibration harmonic. /endulum with either mass 5m6 hangs on a rope 5l6

swing hae a byway angular ϑ o! a balanced. %he restoring !orce is a component style

strap perpendicular.

8 9 ; m g sin <

8 9 m a

So that,

m a 9 ; m g sin <

a 9 ; g sin <

%o ibration com!ormable < it is ery small, so Sin < 9 < byway bow s 9 l < or < 9s

l

so, e)uation becomes a9g . s

lwith e)uation the period ibration harmonic&

= 9 $ >2 L ? %2

%9 t?n

0here,

l 9 length o! rope 5meter6

g 9 accelerate graity 5m?s26

t 9 period o! pendulum 5s6 @2

oing body harmonious simple in swing simple haing a period o!. %he period swing

5% 6 is the time needed assets to do one ibration. (bjects said do one ibration i! moing

objects !rom the points in which the pac+age began to moe and bac+ again to the point.

A unit o! the period is se+on or seconds.


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Amplitude is the measurement o! scalar who non negatie o! large oscillations a waes.

Amplitude can also de!ined as the distance !allen !rom a line e)uilibrium in a wae o!

sinusoide that we learn in the subject and mathematical physics. In pendulum

mathematical, a period and !re)uency a corner in the pendulum simple not dependent on

mass pendulum, depending on penjang ropes and the acceleration o! graity local @3

8rom a !ormula aboe seen that a period o! simple pendulum does not depend on a mass

and a byway pendulum, but only depend on long o! rope and the acceleration o! graity.

athematical pendulum moes !ollow harmonic motion. /endulum simple

5 mathematical 6 ideal is objects consisting o! a mass point, who hangs on a lightweight

rope could not !orward. I! drawn to side pendulum !rom a position balanced

5daid,#BCD

athematical pendulum is a pendulum with long l and mass m and ma+e ghs with a small

angle 5


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Activity 3

#. anipulation ariable & length o! rope 5cm6

2. 'ontrol ariable & mass o! pendulum 5gr6, deiation 5o?cm6, number o!

oscillation

3. Eespons ariable & period o! oscillation 5s6

%/erational -efinition of .ariables

Activity 1

#. ariabel manipulasi & -eiation 5o?cm6

A byway been the large the angle !ormed by pendulum mathematical when pendulum

in pull +esamping measured the use o! the bow degrees with a unit o! degrees 5 6. A⁰

byway is the ariable manipulation because a byway in the !irst actiity changeable

and is ariables a!!ecting ariable response.

2. ariabel +ontrol & Length o! rope 5cm6, mass o! pendulum 5gr6, number o!

oscillation

%he length o! the rope is a long thread used to hang pendulum mathematical in stati!,

measured by point o! piot swing up in a !astener burden use o! # m bar in parts cm.

ass pendulum 5gram the burden who was hanged in the rope measured use the

balance ohauss 3## grams with grams. %he number o! swing is the )uantity o! motion

commuting between done by pendulum when gien a byway and then released. %he

length o! the rope, mass burden, and the number o! swing is the ariable control

because this ariable not changeable or in the state o! remaining.

3. ariabel respon & /eriod o! oscillation 5s6

%he period swing is great the time it ta+es pendulum to do once swing measured use a

stopwatch in parts se+on. (btained !rom time diided by the number o! swing. %his

ariable is the ariable response because the situation in!luenced by ariable

manipulation

Activity 2

#. anipulation ariable & ass o! pendulum 5gr6

ass o! pendulum 5gr6 the burden suspended in the rope measured used the balance

ohauss 3## gram with grams. Is the ariable manipulation because a!!ect the state o!

the response

2. 'ontrol ariable & Length o! rope 5cm6, deiation 5o?cm6

%he length o! the rope is a long thread used to hang pendulum mathematical in stati!,

measured by point o! piot swing up in a !astener burden use o! # m bar in parts cm. A

byway been the large the angle !ormed by pendulum mathematical when pendulum in

pull to side measured the used o! the bow degrees with a unit o! degrees 5 6. %he⁰

number o! swing a motion bac+ and !orth done pendulum mathematical with # times


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swing. %he length o! the rope, a byway, and the number o! swing is the ariable

control because this ariable not changeable or in the state o! remaining

3. Eespons ariable & /eriod o! oscillation 5s6%he period swing is the amount o! time that used pendulum mathematical in doing #

times motion bac+ and !orth, measured use a stopwatch in parts se+on. ariabel this is

the ariable response because the situation in!luenced by ariable manipulation.

Activity 3

#. anipulation ariable & Length o! rope 5cm6

%he length o! the rope is a long thread used to hang pendulum mathematical in stati! ,

measured !rom the point hang 5 a sha!t swing until in a !astener burden use o! # mm

bar in parts cm. ariable this is the ariable manipulation because a!!ect the state o!

ariable response.

2. 'ontrol ariable & ass o! pendulum 5gr6, deiation 5o?cm6, number o!

oscillation

ass pendulum is mass a burden 5pendulum6 who was hanged use thread measured

use the balance ohauss 3## grams with grams. A byway been the large the angle

!ormed by pendulum mathematical !rom the balance point who was hanged with a

thread, measured the use o! the bow degrees with a unit o! degrees 5 6. %he number o! ⁰

swing a motion bac+ and !orth done pendulum mathematical. %o these actiities there

are # times swing. ass pendulum, a byway, and the number o! swing is the ariable

control because this ariable not changeable or in the state o! remaining.

3. Eespons ariable & /eriod o! oscillation 5s6

%he period swing is the amount o! time that used pendulum mathematical in doing #

times motion bac+ and !orth, measured use a stopwatch in parts se+on.ariabel this is

the ariable response because the situation in!luenced by ariable manipulation.

ork Procedure

Activity 1

8irst, weighed mass pendulum 5the load to be suspended in stati!6. Second, /endulum

hanging with a rope 5D cm6 in stati! and gien a byway as many as !ie times 5with a

byway distinct6 such as& D, , B, ##, #3. %hen pendulum released, they measured the time

it ta+es pendulum to swing # times by swing and noted in table obseration

Activity 2

8irst, weighed mass pendulum 5the load to be suspended in stati!6. Second, /endulum

hanging with a rope 5D cm6 in stati! and gien deiation as many as D ⁰. ass pendulum

changed as many as D times 5the length o! the rope and a byway in constant6. /endulum


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released, they measured the time it ta+es pendulum to swing # times by swing and noted

in table obseration

Avtivity 3

8irst, gien a byway as much as D, is used mass pendulum that is !ixed to any long a rope

di!!erent. Second, the length o! the rope changed as many as !ie times that is D cm, $D

cm, $ cm, 3D cm, 3 cm 5mass pendulum and a byway in constant6 and then, pendulum

released they measured the time it ta+es pendulum to swing # times by swing and noted

in table obseration

%BS*&.A'I%( &*SUL' A(- -A'A A(AL+SIS

%bservation &esult

Activity 1. Eelation between deiation and period

Length o! rope 9 JD, K ,DJ cm

ass o! pendulum 9 JBC,B$ K ,DJ gr

Number o! oscillation 9 # times

Tabel 1. %he in!luence deiation to period o! oscillation

Deviation (o/cm) %ime 5s6JD K ,DJ |14,6 ± 1|J K ,DJ J#$,C K #J

JB K ,DJ J#D, K #J

J## K ,DJ J#D,2 K #J

J#3 K ,DJ J#D,$ K #J

Activity 2. Eelation o! mass pendulum with period o! oscillation

Length o! rope 9 JD, K ,DJ cm

-eiation 9 JD, K ,DJ 5 ?cm6⁰


Tabel 2. %he in!luence mass pendulum with period o! oscillation

ass o! pendulum5gram6

%ime 5s6

J#,3 K ,DJ J#$,G K #J

J2,3 K ,DJ J#$,C K #J

JD,D K ,DJ J#D, K #J

JBC,B$ K ,DJ |15,2 ± 1|J#,$ K ,DJ |15,6 ± 1|

Activity 3

ass o! pendulum 9 JBC,B$ K ,DJ gr

-eiation 9 JD, K ,DJ 5 ?cm6⁰



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Tabel 3. %he in!luemce length o! rope to poeriod o! oscillation

/anjang tali 5cm6 0a+tu 5s6

|50,00 ± 0,05| J#2,2 K #J|45,00 ± 0,05| J#$,$ K #J|40,00 ± 0,05| J#3, K #J|35,00 ± 0,05| J#2,2 K #J|30,00 ± 0,05| |11,2 ± 1|

-ata Analysis

:ased on table #, 2 and 3 we can conclude !actors a!!ecting the period swing namely the

length o! the rope, while a deiation, and a mass pendulum did not a!!ect large the period

swing pendulum. Large a deiation did not a!!ect the period swing pendulum on the

condition deiation 5"#$⁰6 .%he crowd also did not a!!ect large the period swing

pendulum, the mass also did not a!!ect large the period swing pendulum, it has been

proen because the wor+ o! the second sight the time it ta+es pendulum mass o! # gram,

2 grams o!, D grams o!, BC gram and # grams need the time which not similar to do

swing # times by with deiation and the length o! the rope same.

Analysis dimensions e)uation % to pendulum mathematical

T=2π

√lg

% is unit o! se+on 5s6 with dimension o! %

T = 2π√ lgs = 2π √mm/s²

2> is constant and don7t haing a unit.

[T ]=√ [ L]

[ L ] [T ]−2

[T ]=√1

[T ]−2

[T ]=√ [T ]2

[T ]=[T ]

8rom the analysis dimensions can be expressed that the e)uation % to mathematical

pendulum is true.


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g 9 B.C m?s2

#6 According to the theory

T1 = 2π√l1g

T 1 = 2 ×22

7 √0.5 m9 .8 m/s²T 1 = 6 .2857 × 0 .2258 s

%# 9 #.$#B3 s

∆T1 =

|∆l1

2 l1

|T1

∆T1 =|0.00052 × 0.5 |1.4193∆T1 9 .D #.$#B3

∆T1 9 .# s

K=∆T1

T1 ×100!

= 0.00711.4193

×100!

9 .D # M

9 .D M 5$ A:6

- 9 # M ; E

9 # M ; .D M

9 BB.BD M

/8 9 |T1" ∆T1| s

9 | 1 4.19 " 0. 0 07 |10-1 s

9 | 1 4.19 " 0. 0 1 |10-1 s

26 According to practicum

t#9 #D.2 s

n 9 # times

T1 =t1

n =

15.2

10 = 1.52 s


10/20

∆T1 = |∆t1t1 |T1=|0.115.2| 1 .52

9 .GG #.D2

9 .# s

K=∆T1

T1 ×100!

=0.01

1.52

×100!

9 .GG M 5$ A:6

- 9 # M ; E

9 # M ; .GGM

9 BB.3$ M

/8 9 |T1" ∆T1| s

9 | 15.2 " 0.1 |10-1 s

b. %he oscillation period !or the length o! string 2

%he length o! string 9 $Dcm 9 .$D m

g 9 B.C m?s2

#6 According to theory

T2 = 2π√l2g

T 2 = 2 ×22

7 √0 .45 m9 .8 m/s²T 2 = 6 .286 ×0.2143 s

%29 #.3$ s

∆T2 =|∆l22 l2 |T2∆T2 =|0.00052 × 0.45 |1.347∆T2 9 .DD #.3$

∆T2 9 .$ s


11/20

K=∆T2

T2 ×100!

=0.00074

1.347 ×100!

9 .DD # M

9 .D M 5$ A:6

-9 # M ; E

9 # M ; .DM

9 BB.BD M

/8 9 |T2" ∆T2| s9 | 13.47 " 0 .007 |10-1 s

9 | 13.47 " 0.01 |10-1 s


t29 #$.$ s

n 9 # times

T2 =t2

n =

14.4

10 = 1.44 s

∆T2 = |∆t2t2 |T2=|0.114.4 | 1 .44

9 .GB #.$$

9 .# s

K=∆T2

T2 ×100!

=0.01

1.44 ×100!

9 .GB M 5$ A:6

- 9 # M ; E

9 # M ; .GBM

9 BB.3# M

/8 9 |T2" ∆T2| s


12/20

9 | 14.4 " 0 .1 |10-1 s

c. %he oscillation period !or the length o! string 3

%he length o! string 9 $ cm 9 .$ m

g 9 B.C m?s2


T3 = 2π√l3g

T 3 = 2 ×22

7 √0.40 m9 .8 m/s²T 3 = 6 .286 × 0 .2020 s

%39 #.2GBB s

∆T3 =|∆l32 l3 |T3∆T3 =|0.00052 × 0.40 |1.2699∆T3 9 .G2D #.2GBB

∆T3 9 .B s

K=∆T3

T3 ×100!

=0.00079

1.2699 ×100!

9 .G2 # M

9 .G2 M 5$ A:6

- 9 # M ; E

9 # M ; .G2 M

9 BB.B$ M

/8 9 |T3" ∆T3| s

9 | 12.69 " 0. 01 |10-1 s


t39 #3 s

n 9 # times


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T3 =t 3

n =

13

10 = 1.30 s

∆T3 = |∆t3t3 |T3=|0.113 | 1 .30

9 . #.3

9 .# s

K=∆T3

T3 ×100!

=0.01

1.30 ×100!

9 . M 5$ A:6

- 9 # M ; E

9 # M ; . M

9 BB.23 M

/8 9 |T3" ∆T3| s

9 | 13.00 " 0.1 |10-1 s

d. %he oscillation !or the length o! string $

%he length o! string 9 3D cm 9 .3D m

g 9 B.C m?s2

#6 According theory

T 4 = 2π√l4

g

T 4 = 2 ×22

7 √0 .35 m9. 8 m/s²T 4 = 6. 286 × 0.1889 s

%$9 #.#C$ s

∆T4 =|∆l42 l4 |T4


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∆T4=|0.00052 × 0.35|1.1874∆T4 9 .#$ #.#C$

∆T4 9 .CD s

K=∆T4

T4 ×100!

=0.00085

1.1874 ×100!

9 .#D # M

9 .#D M 5$ A:6

- 9 # M ; E

9 # M ; .#DM

9 BB.B3 M

/8 9 |T4 " ∆T4| s

9 | 11.87 " 0 .01 |10-1 s


t$9 #2.2 s

n 9 # times

T4 =t4

n =

12.2

10 = 1.22 s

∆T4 = |∆t4t4 |T4=|0.112.2| 1 .22

9 .C2 #.22

9 .# s

K=∆T4

T4 ×100!

=0.01

1.22 ×100!

9 .C2 M 5$ A:6

- 9 # M ; E

9 # M ; .C2M


15/20

9 BB.#C M

/8 9 |T4 " ∆T4| s

9 | 12.2 " 0.1 |10-1 s

e. %he oscillation period !or the length o! string D

%he length o! string 9 3 cm 9 .3 m

g 9 B.C m?s2


T 5 = 2π√l5g

T 5 = 2 ×22

7 √0 .30 m

9 .8 m/s²

T 5 = 6 .286 × 0.1749 s

%D9 #.BBC s

∆T5 =|∆l52 l5 |T5∆T5 =

|0.0005

2 × 0.30

|1.0998

∆T5 9 .C3 #.BBC

∆T5 9 .B2 s

K=∆T5

T5 ×100!

=0.00092

1.0998 ×100!

9 .C3G # M

9 .C$ M 5$ A:6

- 9 # M ; E

9 # M ; .C$DM

9 BB.B2 M

/8 9 |T5" ∆T5| s

9 | 10.99 " 0. 01 |10-1 s


tD9 ##.2 s


16/20

n 9 # times

T5 =

t 5

n =11.2

10 = 1.12 s

∆T5 = |∆t5t5 |T5=|0.111.2| 1.12

9 .CB #.#2

9 .# s

K =∆T5

T5 ×100!

=0.01

1.12 ×100!

9 .CBM 5$ A:6

- 9 # M ; E

9 # M ; .CBM

9 BB.## M

/8 9 |T5" ∆T5| s

9 | 11.20 " 0 .1 |10-1 s

%able $. relation the period o! pendulum mathematical on the actiity 3

The length of

t!ing (m) Time () #$%&'d T =

t

n (s) #$%&'d T= 2π√ lg (s)

| 0"50 ± 0"0005 | | 15"2 ± 1 | | 14.19 " 0.01 |10-1 | 15.2 " 0.1 |10-1 | 0"45 ± 0"0005 | | 14"4 ± 1 | | 13.47 " 0.01 |10-1 | 14.4 " 0.1 |10-1 | 0"40 ± 0"0005 | | 13"0 ± 1 | | 12.69 " 0.01 |10-1 | 13.0 " 0.1 |10-1

| 0"35 ± 0"0005 | | 12"2 ± 1 | | 11.87 " 0.01 |10-1 | 12.2 " 0.1 |10-1 | 0"30 ± 0"0005 | | 11"2 ± 1 | | 10.99 " 0.01 |10-1 | 11.2 " 0.1 |10-1

/lot on graph relation between %2 dan l

%he period according to the theory to the e)uation a period o! mathematical pendulum

%abel D. Eelation %2 with l

#o" The length of t!ing

(m)

T2 (2)

1" 0"50 2"0144


17/20

2" 0"45 1"$1443" 0"40 1"6126

4" 0"35 1"40%%5" 0"30 1"20%6

=raph #. Eelation %2 with l

1"1 1"2 1"3 1"4 1"5 1"6 1"& 1"$ 1"% 2 2"1

0

0"1

0"2

0"3

0"4

0"5

0"6

!5x6 9 .2Dx ;

EO 9 #

Relation T2 with l

/eriod %25s26 Linear 5/eriod %25s266

'he /eriod ' 1s

The length of string l (m)

Acceleration o! graity !rom the graphic plot

T = 2π √ lgT2 = 4π²

l

g

g 9 $ π²l

T²

in the graphic we get &

m=∆

∆ =

l

T ²

so, the e)uatioan acceleration o! graity is &

g = m4π²

y 9 mx P c

y 9 .2$Cx P .

so, m 9 .2$C, the alue o! g is &


18/20

g = 0 .24 8 × 4 ( 227 )2

*/m

= 0.248 ×1936

49 */m = 9.79 m/s2

!ind ∆g by graph &

E 29 #

- 9 #M E 2

- 9 #M # 9 # M

E 9 #M ; -

9 #M ; # M9 M 5$ A:6

K=∆g

g ×100!

∆g=K ×g

100! =

0! ×9+79

100! = 0.00 m/s2

/8 9 J g K ∆g J

/8 9 J B.B K . J m?s2

*,PLA(A'I%(%he !irst actiity is pendulum mathematical, in the !irst actiity will be conducted 3 main

actiities which were o! the in!luence o! a byway to the period. Actiities will be done by

giing a byway in pendulum !ie times, a byway used started !rom D degrees, then

degrees, B degrees, ## degrees, #3 degrees. A!ter doing these actiities we get that the

time needed pendulum to swing # times by on each a byway only a distinct .2 s o!

direct obseration can be concluded that a byway gien has not been a!!ecting the large

the period swings on pendulum mathematical.

%he wor+ o! the second, gonna proe the in!luence o! mass load against the period swing,

to these actiities proided D !ruit load with heay di!!erent namely # grams, 2 grams

o!, D grams o!, BC grams, and # grams. :ut a!ter conducted lab wor+ is almost any

load haing the same time to do swing haing only the time di!!erence .2 s this proes

that mass an expense not a!!ect the period swing

%he wor+ o! the third namely the in!luence o! the length o! the rope to the period swing,

to these actiities we hung load with a rope conerted in length as many as D times 5 mass

burdens and a byway constant6, a!ter doing lab wor+ we can identi!y the e!!ects the length

o! the rope to the period swing , because the more we add the length o! the rope so the


19/20

period swing pendulum also will be bigger .%he length o! the rope !irst is JD, K ,DJ

cm, the period according to theory isJ#$,#B K ,#J #;# s and according to obseration

result the period is J#D,2 K ,#J #;# s. Length o! second rope is J$D, K ,DJ cm, the

period according theory is J#3,$ K ,J #;# s and according to obseration result the

period is J#$,$ K ,#J #;#s. %he length o! third rope is J$, K ,DJ cm, the period

according to theory is J#2,GB K ,#J #;# s and according to obseration result the period

is J#3, K ,#J#;# s. %he length o! !ourth rope is J3D, K ,DJ cm, the period according

theory is J ##,C K ,#J#;# s and according to obseration result the period is J#2,2 K ,# J

#;#s. %he length o! !i!th rope is J3, K ,DJ cm, the period according theory is J#,BB K

,#J #;# s and according to obseration result the period is J##,2 K ,#J #;#s. I!

compared between the calculation on a period o! using !ormulas %9t

n with this

!ormulas T=2π √ lg the result is not distant di!!erent. So can be concluded that thedata obtained !rom the lab wor+ is in line with the theory that is. 8rom obseration result

obtained the alue o! the acceleration o! graity o! B,B m?s2. According to the theory

large the acceleration o! graity B.C m?s2 so that the experiment this can be assessed as

being success!ul

3%(3LUSI%(

A!ter doing lab wor+ can be concluded that !actor that in!luences large the period swings

on pendulum mathematical is the length o! the rope. ass and deiation did not a!!ect the

period swing. %hrough a method o! swing simple we can determine large the acceleration

o! graity using !ormulas T=2π√ lg to pendulum mathematical&*F*&*(3*

@#academia.edu?G$$B3C3?LaporanQ/enelitianQenghitungQ/ercepatanQ=raitasiQdenga

nQengguna+anQ:andulQatematis

@2 :a+ti,S.2. Desain Instrument Elektronik untuk Mengukur ravitasi uatan

dengan /rinsip !andul matematis. ataram& =raity

@3 Halliday.2D. 8isi+a dasar. Ra+arta& rlangga


20/20

basic physic report pendulum (fix)

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