A-LevelPhysicsOscillations9702/42 · Oct/Nov 2017 · Q38 Marks

(b) A thin metal strip, clamped horizontally at one end, has a load of mass M attached to its free end, as shown in Fig. 3.1. [Figure 3.1] The metal strip bends, as shown in Fig. 3.1. When the free end of the strip is displaced vertically and then released, the mass oscillates in a vertical plane. Theory predicts that the variation of the acceleration a of the oscillating load with the displacement x from its equilibrium position is given by a = – ( c / ML³ ) x where L is the effective length of the metal strip and c is a positive constant.

(a)(i)Define the radian.[2]
(a)(ii)State, by reference to simple harmonic motion, what is meant by angular frequency.[1]
(b)(i)Explain how the expression shows that the load is undergoing simple harmonic motion.[2]
(b)(ii)For a metal strip of length L = 65 cm and a load of mass M = 240 g, the frequency of oscillation is 3.2 Hz. Calculate the constant c. c = .............................. kg m³ s⁻²[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.

[1] (a)(i) angle (subtended) where arc (length) is equal to radius
[1] (a)(i) (angle subtended) at the centre of a circle
[1] (a)(ii) angular frequency = 2π × frequency or 2π / period
[1] (b)(i) c/ML³ is a constant so acceleration is proportional to displacement
[1] (b)(i) minus sign shows that acceleration and displacement are in opposite directions
[1] (b)(ii) c/ML³ = (2πf)²
[1] (b)(ii) c = 4π² × 3.2² × 0.24 × 0.65³
[1] (b)(ii) = 27 kg m³s⁻²

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