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Date	May 2019	Marks available	3	Reference code	19M.3.HL.TZ1.11
Level	Higher level	Paper	Paper 3	Time zone	1
Command term	Determine	Question number	11	Adapted from	N/A

Question

The graph shows the variation with time t of the total energy E of a damped oscillating system.

The Q factor for the system is 25. Determine the period of oscillation for this system.

[3]

Another system has the same initial total energy and period as that in (a) but its Q factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.

[1]

Markscheme

ALTERNATIVE 1

« $Q = 2\pi \frac{{{E_0}}}{{{E_0} - {E_1}}} » \Rightarrow {E_1} = \left( {1 - \frac{{2\pi }}{Q}} \right){E_0}$ ✔

${E_1} «= \left( {1 - \frac{{2\pi }}{{25}}} \right) \times 12» = 9.0$ «mJ» ✔

reading off the graph, period is 0.48 «s» ✔

Allow correct use of any value of E₀, not only at the time = 0.

Allow answer from interval 0.42−0.55 s

ALTERNATIVE 2

use of $Q = 2\pi f\frac{{{\text{energy stored}}}}{{{\text{power loss}}}}$ ✔

energy stored = 12 «mJ» AND power loss = 5.6 «mJ/s»✔

«f = 1.86 s so» period is 0.54 «s» ✔

Allow answer from interval 0.42−0.55 s.

Award [3] for bald correct answer.

similar shape graph starting at 12 mJ and above the original ✔

Examiners report

Q factor. Most of the candidates attempted to find the period of the damped system by using the correct formula.

Many thus went on to establish the correct period within the range given. Some candidates made POT errors not recognizing or identifying the unit used in this question.

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)

Option B: Engineering physics

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