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Date	November 2019	Marks available	1	Reference code	19N.3.HL.TZ0.10
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Describe	Question number	10	Adapted from	N/A

Question

A pendulum bob is displaced until its centre is 30 mm above its rest position and then released. The motion of the pendulum is lightly damped.

Describe what is meant by damped motion.

[1]

a.

After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the Q factor.

[1]

b.

The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.

When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.

[2]

c.

Markscheme

a situation in which a resistive force opposes the motion
OR
amplitude/energy decreases with time ✔

a.

$Q = 2 π \times \frac{30}{30 - 28} = 94.25 \approx 94$ ✔

b.

$94 = 2 π \times 0.80 \times \frac{0.020}{power loss}$ ✔

power added = $1.1 \times 10^{- 3}$ «W» ✔

c.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics) » B.4 – Forced vibrations and resonance (HL only)

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Option B: Engineering physics » Option B: Engineering physics (Additional higher level option topics)

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