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

Damped and forced oscillations, resonance — practice question

A metal block is suspended vertically from one end of a spring, while the spring’s other end is fastened to a thread that runs over a pulley and is connected to a vibrator, as illustrated in Fig. 4.1.
(a(i))[2]

With the vibrator turned off, the $120\,\text{g}$ metal block is moved vertically and let go. Fig. 4.2 shows how the displacement $y$ of the block from its equilibrium position changes with time $t$. For the block’s vibrations, calculate the angular frequency $\omega$.

(a(ii))[2]

For the block’s vibrations, calculate the energy of the vibrations.

(b)[3]

The vibrator is now turned on. The vibration frequency is changed from $0.7f$ to $1.3f$, where $f$ is the block’s vibration frequency in (a). For the block, complete Fig. 4.3 to show how the amplitude of vibration varies with frequency. Label this line A.

(c)[2]

Some light feathers are now added to the block in (b) so that air resistance increases. The vibration frequency is again varied from $0.7f$ to $1.3f$. The new amplitude of vibration is recorded for each frequency. On Fig. 4.3, draw a line to show how the amplitude of vibration varies with frequency. Label this line B.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Uses $T = 0.60\,\text{s}$ together with $\omega = 2\pi/T$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI