10. Oscillations

Question 1

state 2 conditions necessary for a mass to be undergoing simple harmonic motion

Answer 1

1. acceleration is proportional to displacement from equilibrium
2. acceleration is directed towards equilibrium OR displacement and acceleration in opposite directions

Question 2

acceleration a of tube is given by” a= - (Aph/M)x
where x is vertical displacement of tube from eqm position

use the expression to explain why the tube undergoes SHM in liquid

Answer 2

A, p, g, M are constant
hence, acceleration is proportional to displacement from eqm
-ve sign indicates a and x are in opposite directions

Question 3

explain how an acceleration-height graph of a vertical mass-spring system shows that it is undergoing SHM

Answer 3

straight line indicates acc is directly proportional to displacement from eqm
negative gradient shows acc and displacement are in opposite directions

Question 4

explain how an acceleration-displacement FROM EQUILIBRIUM graph of a vertical mass-spring system shows that it is undergoing SHM

Answer 4

straight line CUTTING THROUGH ORIGIN indicates acc is directly proportional to displacement from eqm
negative gradient shows acc and displacement are in opposite directions

Question 5

explain what is meant by the natural frequency of the system

Answer 5

frequency at which the body oscillates when there is no external driving force or resistive force on it

Question 6

for an oscillating body, explain what it means by forced frequency

Answer 6

frequency at which an object is FORCED to oscillate/vibrate

Question 7

distinguish between free oscillations and forced oscillations

Answer 7

free: body oscillates without any resistive forces and external forces applied
forced: continuous energy input to a body by an external periodic driving force to vibrate the body

Question 8

for an oscillating body, state what it means by resonance

Answer 8

1. maximum transfer of energy from driver to oscillator
2. maximum amplitude of vibration in oscillating body
3. when forced frequency = natural frequency

Question 9

state and explain one situation where resonance is useful

Answer 9

vibration of quartz/ piezoelectric crystal

for accurate timing (or maximise amplitude of ultrasound waves)

Question 10

state and briefly explain one other situation in which resonance should be avoided

Answer 10

• metal panels on a machinery oscillate
• motor in machine impresses frequency on panel
  OR
• car suspension system oscillates
• going over bumps would give large amplitude vibrations