examples of pendulum and spring problems answer key
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Examples of
Period Frequency
Problems
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Frequency and Period Problem(Without Period or Frequency given)
Terry Jumps up and down on a
trampoline 30 times in 55 seconds.
What is the frequency with which he
is jumping?
30 times
55 seconds
0.55 Hz
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Frequency and Periodonversion !roblem
Terry Jumps up
and down on a
trampoline witha frequency of
1.5 !. What is
the period ofTerry"s jumping?
".5 Hz
0.#$ sec
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Examples of
Pendulum
Problems
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#ro$lem%
& 't the (alifornia 'cademy of )ciences the
length of the pendulum is%
%0m & '
& The acceleration of gra*ity at this location is%
%. mss & g
& What is the #eriod? *&++++ seconds
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)olution
'ist,' & %0m
g & %. mss
*&++++ seconds
(hoose equation%
)ol*e% +#lug and (hug,
90 m
9.8 m/s/s
9.18 s2
(3.03 s )
(19.0 s )
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- !endulum has a length o 3 m ande/ecutes 0 com!lete vibrations in
$0 seconds.
Find the acceleration o gravity atthe location o the !endulum.
A problem where you
Find the period or frequeny 1st
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- !endulum has a length o 3 m ande/ecutes 0 com!lete vibrations in $0
seconds. Find g.". & cycles seconds
& 0 cycles $0 seconds
& 0.# hz & 0.# sec .
* & " & (" 0.#) seconds & 3.5 seconds
What short cut could - ha*eused?
# vibrations
# seconds is
the time for allthe
oscillations
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' & 3m and *& 3.5 secondsFind the acceleration o gravity at the location
3.5 s & 12(3g)
3.5 s & #. 2(3g)
quare both sides".5 & 3%.43 (3g)
".5 & "".3g
".5(g) & "".3
ivide by ".5
g & %.#5 mss
Heads up!!
If you ÷ by 2π
Use (2π ) !!
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' pro$lem Where
6g6 & %. mss is 7understood89no: you use g&%. mss i,
7g8 not given or as;ed or used %. mss
Part ", - sim!le !endulum has a !eriod o .400
seconds :here 6g6 & %."0 mss. Find the length+
Part , Find 6g6 :here the !eriod o the same!endulum is .4"0 seconds at a dierent location.
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Why are the items green on this pro$lem??
#endulum is not a *aria$le
why is it mar/ed??& - sim!le !endulum has a !eriod o .400
seconds :here 6g6 & %."0 mss. Find the
length+
& Find 6g6 :here the !eriod o the same!endulum is .4"0 seconds at a dierent
location.
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1st find the ength- sim!le !endulum has a !eriod o .400 seconds
:here 6g6 & %."0 mss.
T24 6g7
.002 4 68.9107
.002 38. 68.9107
.008.9107 2
38.
'&".433 m
& Write equation
& )u$stitute :"s
& )quare 4
& ; 38.
'nd < 8.910
& -ns:er :ith
label
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Part ,
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Examples ofSpring
ProblemsHooke’s Law
graphing
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Examples ofusing the graph
to nd the Slopeand the !alue of "k#for springs
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What is the spring
constant for the data
graphed $elow?
Δx(m
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(0=0)
(6,147)
(2,49)
y @ y"
/@/"!lope "
"4$> A 4%>
# m A m
# "
% >
4 m
# "
# " 2$.% &/m'ow do #now the *bel++
*bels on *,es- ise (&) un (m)
!o- rise/run is &/m
Δx(m )
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Examples ofSpring
Problems
$singEquations
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/Hoo;eCs 'a: !roblems
tretch or com!ress A at rest-n anticipation of her first game 'lesia pulls $ac/the handle of a pin$all machine a distance of
5.0 cm. The force constant is 00 >6m. owmuch force must 'lesia eert?
B l H ; C ' bl
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B/am!les o Hoo;eCs 'a: !roblems
List%&x ' ()* cm ' )*( m
k ' +** ,-mFsp'...
-n anticipation of her first game 'lesia pulls $ac/ the handle of a pin$all machine
a distance of 5.0 cm. The force constant is 00 >6m. ow much force must
'lesia eert?
@sp
2 / A
@sp2 00>6m0.05 m7
@sp2 10>
=quation
)u$stitute :"s
'nswer with la$el
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B/am!le o ?scillation s!ringProblems
?scillating or bouncing & Bianca stands on a $athroom scale which
has a spring constant of 0 >6m. Theneedle is $ouncing from side to side.
Bianca"s mass is 190 /g. What is the period
of the *i$rating needle attached to the
spring?
B am!le o ?scillation & Bianca stands on a $athroom scale
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B/am!le o ?scillation!ring
Problem
& Bianca stands on a $athroom scale
which has a spring constant of 0
>6m. The needle is $ouncing from
side to side. Bianca"s mass is 190
/g. What is the period of the
*i$rating needle attached to the
spring?'ist, ; & 0 >m
m & "0 ;g
* & ++
"0 ;g
0>m
0." s
(0.%04 s)
5.$ sec
Spring Problems
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Spring ProblemsUse Both Equations
Example of /ombination of
Hooke’s Law and 0scillation of spring@ind / from oo/e"s aw and then use the
oscillation equation
'utumn a young 0 ;g girl is playing on atrampoline. The trampoline sin/s down % cm whenshe stands in the middle. What is the s!ring
constant+
-f the trampoline then $egins to $ounce :hat :ouldthe requency o the bounces be+
'utumn a young 0 /g girl is playing
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"st Find Force o Dravity on mass
nd Find ; rom Hoo;eCs 'a:
3rd use the oscillation equation toind *
4th convert to Frequency
'utumn a young 0 /g girl is playing
on a trampoline. The trampoline sin/s
down 8 cm when she stands in the
middle. What is the s!ringconstant+
-f the trampoline then $egins to$ounce :hat :ould the requency
o the bounces be+
'ist , m & 0 ;g
Δx = 9 cm = 0.09m
f =
!he P"#$% Using &oo'e(s "a) an*
+scillation of spring
Fg& m ag
Fs!& ; E/
'utumn a young 0 /g girl is playing
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'utumn a young 0 /g girl is playing
on a trampoline. The trampoline sin/s
down 8 cm when she stands in the
middle. What is the s!ringconstant+
'ist , m & 0 ;g
Δx = 9 cm =0.09 m
f =
Using&oo'e(s "a) , +scillation of
spring
"st
Find Force o Dravity on mass
Fg& m ag
Fg& 0;g(@%.mss)
Fg& @ "%# >
ecall
From the FG on the 'ab
F & "%# >?. . .
'utumn a young 0 /g girl is playingExample of ombination of
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'utumn a young 0 /g girl is playing
on a trampoline. The trampoline sin/s
down 8 cm when she stands in the
middle. What is the s!ringconstant+
'ist , m & 0 ;g
Δx = 9 cm =0.09 m
-s= 9/ $
f=
Example of ombination of&oo'e(s "a) an* +scillation of
spring
nd Find ; rom Hoo;eCs 'a:
Fs!& ; E/
"%# > &;(0.0%m)
"0 >m & ;
'utumn a young 0 /g girl is playing on aExample of ombination of
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'utumn a young 0 /g girl is playing on a
trampoline. The trampoline sin/s down 8 cm
when she stands in the middle. What is the
spring constant?
-f the trampoline then $egins to $ounce :hat
:ould the requency o the bounces be+
'ist , m & 0 ;g
Δx = 9 cm =0.09 m
Fs& "%# >
' = 120 $3m
! =
f =
Example of ombination of&oo'e(s "a) an* +scillation
of spring
3rd use the oscillation equation
to ind *
0 ;g
"0 >m
.00%"$ s
(0.%5 s)
.#0 sec
'utumn a young 0 /g girl is playing on a
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'utumn a young 0 /g girl is playing on a
trampoline. The trampoline sin/s down 8 cm
when she stands in the middle. What is the
spring constant?
-f the trampoline then $egins to $ounce wh*t
would the frequeny of the bounes be+
'ist , m & 0 ;g
Δx = 9 cm =0.09 m
Fs& "%# >
' = 120 $3m
! = 0./01 sec
f =
Example of ombination of&oo'e(s "a) an* +scillation
of spring
4th convert to requency
.#0 s
".## Hz
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4 part Spring problemCse @g to find the / *alue and then use same
string with same / to find nd mass.-f two +Drumpy Eld Fen, went ice fishing and werecomparing their fish with the etension of the same
spring sol*e the following spring pro$lem% +Drumpy
)am, caught the first fish and magically reali!ed the fishhad a mass of 3 /g. When this fish was suspended on
the spring li/e the one we suspended masses on in la$
the spring stretched so it was 3 cm longer than it was
without the fish. What is the s!ring constant or thes!ring+ +Drumpy Joe, then caught a fish that causedthe same spring to etend 5 cm from the length of the
empty spring. What :as the mass o 7Drum!yIoeCs8 ish+
-f two +Drumpy Eld Fen, went ice
*he Plan to solve,
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Example of 4 part Springproblem
-f two Drumpy Eld Fen went ice
fishing and were comparing their fish
with the etension of the same spring
sol*e the following spring pro$lem%
+Drumpy )am, caught the first fish and
magically reali!ed the fish had a massof 3 /g. When this fish was
suspended on the spring li/e the one
we suspended masses on in la$ the
spring stretched so it was 3 cm longer
than it was without the fish. What is
the s!ring constant or the s!ring?
'ist , m & 3 ;g
Fg& ++
Δx = 5 cm =0.05 m
-sp =
st
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p p p gproblem
-f two Drumpy Eld Fen went ice
fishing and were comparing their fish
with the etension of the same spring
sol*e the following spring pro$lem%
+Drumpy )am, caught the first fish and
magically reali!ed the fish had a massof 3 /g. When this fish was suspended
on the spring li/e the one we
suspended masses on in la$ the spring
stretched so it was 3 cm longer than it
was without the fish. What is the
s!ring constant or the s!ring+
Fg& m ag
Fg& 3;g(@%.mss)
Fg& @ 5 >
'ist , m & 3 ;g
Fg&
Δx = 5 cm = 0.05m
-sp =
@ 5 > & @ Fs
5 > & Fs
st
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p p p gproblem
-f two Drumpy Eld Fen went ice
fishing and were comparing their fish
with the etension of the same spring
sol*e the following spring pro$lem%
+Drumpy )am, caught the first fish and
magically reali!ed the fish had a massof 3 /g. When this fish was suspended
on the spring li/e the one we
suspended masses on in la$ the spring
stretched so it was 3 cm longer than it
was without the fish. What is the
s!ring constant or the s!ring+
'ist , m & 3 ;g
Fg& @ 5 >
Δx = 5 cm = 0.05m
-sp = 116 $
Fs!& ; E/
5 > &;(0.03m)
$500 >m &;
nd use Hoo;e to ind the ; value
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xamp es o par pr ng rumpy oe4s5 Fish
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p p p gproblem
py
&67 F6
&67 :A!!
-JB PK>DLL
+Drumpy Joe, then caught a fish thatcaused the same spring to etend 5 cm
from the length of the empty spring.
What :as the mass o 7Drum!yIoeCs8 ish+
'ist , m & +++ ;g
Fg& @3$5 >
Δx = 6 cm = 0.06m
-sp = 576 $
' = 7600 $3m
4th convert :eight to mass
Fg& m ag
@3$5 >& m(@%.mss)
m& 3.3 ;g
@ 3$5 > & @ Fs
3$5 > & Fs
E ti
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Equation
Sheet
Sli*esfor
Springsan*
Pen*ulums
#eriod and @requency notes
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#eriod and @requencyGnotes& ert! is unit that means 16sec
& '$$re*iated GGGGGGG !
& Fega ert! H@F radio
& Iilo ert! H 'F radio;*
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#eriod and @requency& ert! is unit that means 16sec
& '$$re*iated GGGGGGG !
& Fega ert! H@F radio
& Iilo ert! H 'F radio
@se when you
#now
either or f
;*
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Escillations for #endulums onlyG>otesength of the pendulum and gra*ity determine how fast
the pendulum oscillates $ac/ and forth.;*
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;*
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!age 4 !ace M3
)prings only
#eriod and @requency
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#eriod and @requency& ert! is unit that means 16sec !7
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oo/e"s aw for )prings only
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)prings only