SHM test

1.       The acceleration of the oscillator is directly proportional to the                              B1
displacement (the term displacement to be included and spelled correctly
to gain the mark).
with the acceleration always directed to a fixed / equilibrium point                        B1

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  2.     (a)     arrow towards centre of planet                                                                         1

(b)     (i)      g = GM/R2                                                                                               1

(ii)     gS/gO = R2/25R2; gS = 40/25 (= 1.6 N kg–1)                                             2

(iii)    gC/gO = R2/16R2 giving gS = 40/16 (= 2.5 N kg–1)                                    1

(iv)    average g = (2.5 + 1.6)/2 = 2.(05) (1)
Δp.e. (= mgavR) = 3.0 × 103 × 2.05 × 2.0 × 107; = 1.2 × 1011 (J) (2)       3

  (c)   g = v2/r; = 4π2(5R)/T2 (2)
1.6 = 4 × 9.87 × 1.0 × 108/T2 giving T2 = 24.7 × 108 and T = 5.0 × 104 (s) (2) 4

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  3.     (a)     (i)      Fig. 1 : x and a in opposite directions/acceleration towards
equilibrium point/AW; (1)
Fig. 2 : proportional graph between x and a/AW (1)                                2
Figures not identified max. of 1 mark

  (ii)   a = 4π2f2x; 50 = 4π2f2.50 × 10–3; giving f2 = 25 and f = 5.0 Hz              3

  (iii)  cosine wave with initial amplitude 25 mm; decreasing amplitude; (2)
correct period of 0.2 s (for minimum of 2.5 periods); (1)                       3

  (b)   (i)      the acceleration towards A/centripetal acceleration or force;
is constant                                                                                               2

  (ii)   a = v2/r; so 50 = v2/10; v2 = 500 giving v = 22.4 m s–1                            3

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  4.     (a)     (i)      v = 2πrf = 2π × 0.015 × 50; = 4.7 (m s–1)                                                2

  (ii)   a = v2/r = 4.72/0.015; = 1.5 × 103 (m s–2) ecf(a)(i)                                   2

  (iii)  the belt tension is insufficient to provide the centripetal force; (1)
so the belt does not ‘grip’ the pulley/does not hold the belt against
the pulley/there is insufficient friction to pull/push/move the belt. (1)    2
alternative argument the belt does not ‘grip’ the pulley/there is
insufficient friction to pull/push/move the belt; because of its
inertia/insufficient to provide force for acceleration of (belt)-drum

  (b)   resonance occurs; when the natural frequency of vibration of the (1)
panel = rotational frequency of the motor (1)                                                   2

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