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

Damped and forced oscillations, resonance — practice question

A long length of springy steel is held firmly at one end, leaving the strip upright. A mass of $65\,\text{g}$ is attached to the free end of the strip, as shown in Fig. 2.1. The mass is displaced to one side and then let go. Fig. 2.2 shows how the horizontal displacement of the mass changes with time $t$. The mass undergoes damped simple harmonic motion.
(a(i))[2]

Explain what the term 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 work out the frequency of vibration of the mass.

(b(ii))[2]

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

(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

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