A-LevelPhysicsOscillations9702/41 · Oct/Nov 2017 · Q29 Marks

State, by reference to simple harmonic motion, what is meant by angular frequency.

(a)State, by reference to simple harmonic motion, what is meant by angular frequency.[1]
(b)(i)1A thin metal strip is clamped at one end so that it is horizontal. A load of mass M is attached to its free end. The load causes a displacement s of the end of the strip, as shown in Fig. 2.1. [Figure 2.1] The load is displaced vertically and then released. The load oscillates. The variation with the acceleration a of the displacement s of the load is shown in Fig. 2.2. [Figure 2.2] Use Fig. 2.2 to determine the displacement of the load before it is made to oscillate,[1]
(b)(i)2the amplitude of the oscillations of the load.[1]
(b)(ii)Show that the load is undergoing simple harmonic motion.[3]
(b)(iii)Calculate the frequency of oscillation of the load.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[B1] (angular frequency =) 2π × frequency or 2π/period
[A1] displacement = 2.0 cm
[A1] amplitude = 1.5 cm
[B1] reference to displacement of oscillations or displacement from equilibrium position or displacement from 2.0 cm
[B1] straight line indicates acceleration ∝ displacement
[B1] negative gradient shows acceleration and displacement are in opposite directions
[C1] ω² = (-)1/gradient or ω² = (-)Δa/Δs or a = (−)ω²x and correct value of x
[C1] = e.g. (1.8/0.03) or (0.9/0.015) or (1.2/0.02) etc. or 0.9 = ω² × 0.015 = 60
[A1] f = √60/2π = 1.2 Hz

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