Physics 9702 · AS & A Level · Damped and forced oscillations, resonance

Damped and forced oscillations, resonance — practice question

A strip of springy steel is fixed at one end so that it stands vertically. A mass of $65\,\text{g}$ is fastened to the loose end of the strip, as shown in Fig. 2.1. The mass is pulled sideways and then let go. Fig. 2.2 shows how the horizontal displacement of the mass changes with time $t$. The mass carries out damped simple harmonic motion.
(a(i))[2]

Explain what damping means.

(a(ii))[2]

Suggest, with a reason, whether the damping is light, critical or heavy.

(b(i))[1]

Use Fig. 2.2 to find the frequency of vibration of the mass.

(b(ii))[2]

Hence show that the initial energy stored in the steel strip before the mass is released is about $3.2\,\text{mJ}$.

(c)[2]

After eight complete oscillations of the mass, the amplitude of vibration falls from $1.5\,\text{cm}$ to $1.1\,\text{cm}$. State and explain whether, after a further eight complete oscillations, the amplitude will be $0.7\,\text{cm}$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Decrease in the energy of oscillations

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