simple harmonic motion oscillatory systems §periodic motion §elasticity §inertia §interchange of...
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Oscillatory SystemsPeriodic motionElasticityInertiaInterchange of energiesExamples:
Mass on helical spring Cantilever Simple pendulum Vertical rod floating in liquid
Characteristics of SHMOccurs in many systemsIsochronous oscillationPossesses springiness (elasticity) to store P.E.Possesses inertia to store K.E.Period of vibration depends on elastic and in
ertia factorsConstant total energy
Conditions for performing SHM acceleration is always directed towards a fixed
point acceleration varies directly as its distance from
the fixed point i.e. in linear motion
in angular motion
x x
Rotating Vector Model
As particle N describes uniform circular motion, its projection point P performs simple harmonic motion
computer simulation
Solving Problems on SHM
Assume displacement x from the mean position
Draw a diagram showing all forcesApply Newton’s second law with appropriate
sign conventionShow that The constant of proportionality = 2
Period T = 2/
x x
Floating Tube in a Liquid (2)
xm
gAx
x
h
g
g
hT 2
Effects of viscosity of liquid:
• causes damping
• takes away K.E. from the oscillating tube
Superposition of Two Harmonic Variations
The amplitude and phase of the resultant is obtained by the parallelogram law
)cos()cos(cos tctbta
Experimental Determination of g (1)
a) A simple pendulum:
gT
22 4
• Plot a graph of T2 vs l
• Slope = g
24
b) A loaded spring:i) The static experiment: Plot the extension-load graph
k
g
m
es 1Slope:
Experimental Determination of g (2)
Experimental Determination of g (3)
ii) The dynamic experiment:
measure the period of oscillation for different loads
ks
2
2
4
22
1
4g
s
s