Oscillations: Question 9

Worked solution

Step 1: Recall the defining feature of light damping

Light damping occurs when a resistive force removes energy from an oscillating system relatively slowly. This causes the amplitude of successive oscillations to decay gradually, oscillation by oscillation, while the period (and hence the frequency) of the oscillation stays almost unchanged from the undamped case, provided the damping is light.

Step 2: Match this to the options

• Option A states that the period stays approximately constant while the amplitude decreases, this matches the defining behaviour of light damping exactly.

Step 3: Check why the other options are wrong

• B: Under light damping the period does not change significantly; a large change in period only becomes noticeable as damping becomes much heavier, and heavy damping does not even produce a regularly repeating oscillation at all. So B is incorrect for the lightly damped case described.
• C: Frequency is not linked to the amount of energy remaining in this way. A lightly damped oscillator’s frequency stays close to its natural (undamped) value throughout the decay, it does not increase as energy is lost.
• D: This describes an idealised, undamped system, where total mechanical energy is conserved and simply interchanges between kinetic and potential stores. Damping, by definition, means the system loses energy overall (usually as heat, dissipated by the resistive force). This is precisely why the amplitude in the graph decreases. So D contradicts the fact that damping is occurring at all.

Final answer

• The correct statement is option A: the period of oscillation stays approximately constant while the amplitude decreases.