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Simple
Harmonic Motion ( continued)
Assessment objectives
By the end of this topic, the student should be
able to:
- Derive the expression a = -w2x
component of acceleration of
a body moving in a circle.
- Define simple harmonic motion.
- Verify that a simple pendulum, a mass at the end
of a string, a liquid
in a U-tube, floating cylinder and car piston oscillate
with SHM.
- Define the terms period and amplitude.
- Derive and use the expression for the period in each
of the above
examples of SHM.
- Verify that the solutions of the equation a =
-w2x are of the form
x = A sin wt or x = A cos wt .
- Explain phase difference between two different simple
harmonic
oscillators.
- Draw sketch graphs to show the variation of displacement,
velocity,
acceleration with time.
- Derive and use the expression v = ± wÖ(A2
- x2 ) for the velocity of a simple
harmonic oscillator.
- Derive and use expressions for potential energy and
kinetic energy of a simple
harmonic oscillator and hence the mechanical energy.
- Describe the interchange between kinetic energy and
potential energy during
SHM and show that mechanical energy is constant.
- Draw a sketch graph to show the variation of P.E
and K.E and mechanical energy
with displacement.
 4.3.2
Damped and Free Oscillations.
 Damped oscillations.
Forced oscillations
and resonance.
Assessment objectives
By the end of this topic, the student should be
able to:
- Distinguish between free and damped oscillations.
- Describe practical examples of damped oscillations
with
- particular reference to the degree of damping and
the importance
- of critical damping in such cases as car suspension
system.
- Explain forced oscillations and describe practical
examples of forced
- oscillations and resonance.
- Describe graphically how amplitude of forced oscillations
varies with
- frequency.
- Define resonance.
- State the factors which determine the frequency response
and sharpness
- of the resonance of a forced oscillator.
- List examples od cases where resonance is useful
and where it is undesirable.
- Perform and describe an experiment to determine acceleration
due to gravity using ;
(i) simple pendulum .
(ii) helical spring .
- Perform an experiment to determine Young's modulus
of wood using a
vibrating wooden beam .
End of S5
Term 2 : Estimated time : 10
weeks ( 9 Periods per week)
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