IB Physics HL C 4 5 Damping and Resonance Questions

Practise IB Physics HL C.4.5 by solving damping, Q-factor, energy-loss and driven-resonance problems across mechanical systems.

Exam points

Calculate Q factor, energy retention and amplitude changes in damped oscillators.
Predict how damping changes resonance-curve height, width and resonant frequency.
Analyse driven and free oscillations in springs, bridges, pendulums and other systems.

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Study C.4.5—Damping and resonance conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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A mass is attached to a vertical spring. The other end of the spring is attached to the driver of an oscillator.

Figure for Question IB Physics HL C 4 5 Damping and Resonance Questions question 1 — IB Physics HL

The mass is performing very lightly damped harmonic oscillations. The frequency of the driver is higher than the natural frequency of the system. At one instant the driver is moving downwards.

The oscillator is switched off. The system has a Q factor of 22. The initial amplitude is 10 cm . Determine the amplitude after one complete period of oscillation.

ALTERNATIVE 1:
$\begin{aligned} & \lessdot Q=2 \pi \frac{A_{0}^{2}}{A_{0}^{2}-A_{1}^{2}} \| \Rightarrow \frac{A_{1}^{2}}{A_{0}^{2}}=1-\frac{2 \pi}{Q} & \frac{A_{1}}{A_{0}}=\lessdot \sqrt{1-\frac{2 \pi}{22}}=» A_{1}=8.5 \lessdot \mathrm{~cm} \| \end{aligned}$

ALTERNATIVE 2:

driver amplitude is constant

so mass amplitude is unchanged at 10 cm

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IB Physics HL C 4 5 Damping and Resonance Questions question 1