Physics (AS & A Level) · Oct / Nov 2016 · Paper 41 · Question 3
9702
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To demonstrate simple harmonic motion, a student attaches a trolley to two similar stretched springs, as shown in Fig. 3.1. spring trolley Fig. 3.1 The trolley has mass m of 810 g. The trolley is displaced along the line of the two springs and then released. The subsequent acceleration a of the trolley is given by the expression a = − 2k x m where the spring constant k for each of the springs is 64 N m−1 and x is the displacement of the trolley.
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3(a)[3]
2k/m = ω2 ω = 2πf (2 × 64 / 0.810) = (2π × f) 2 leading to f = 2.0 Hz [3]
3(b)[2]
v0 = ωx0 or v0 = 2πfx0 or v = ω(x0 2 – x2) 1/2 and x = 0 v0 = 2π × 2.0 × 1.6 × 10–2 = 0.20 m s–1 [2]
3(c)[2]
frequency: reduced/decreased maximum speed: reduced/decreased [2]
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