Physics (AS & A Level) · Oct / Nov 2016 · Paper 42 · Question 4
9702
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A mass hangs vertically from a fixed point by means of a spring, as shown in Fig. 4.1. spring mass l Fig. 4.1 The mass is displaced vertically and then released. The subsequent oscillations of the mass are simple harmonic. The variation with time t of the length l of the spring is shown in Fig. 4.2. 0.1 12 14 16 18 t / s 13 15 17 0.2 0 0.3 0.4 0.5 0.6 l / cm Fig. 4.2
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4(a)(i)[1]
0.225 s and 0.525 s [1]
4(a)(ii)[2]
period or T = 0.30 s and ω = 2π / T ω = 2π / 0.30 ω = 21 rad s–1 [2]
4(a)(iii)[2]
speed = ωx0 or ω(x0 2 – x2) 1/2 and x = 0 = 20.9 × 2.0 × 10–2 = 0.42 m s–1 [2]
or use of tangent method: correct tangent shown on Fig. 4.2 (C1) working e.g. ∆y / ∆x leading to maximum speed in range (0.38–0.46) m s–1 (A1)
4(b)[3]
sketch: reasonably shaped continuous oval/circle surrounding (0,0) curve passes through (0, 0.42) and (0, –0.42) curve passes through (2.0, 0) and (–2.0, 0) [3]
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