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2 July, 00:49

A baby bounces up and down in her crib. Her mass is 13.0 kg, and the crib mattress can be modeled as a light spring with force constant 788 N/m. (a) The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency? Hz (b) If she were to use the mattress as a trampoline-losing contact with it for part of each cycle-what minimum amplitude of oscillation does she require? cm

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  1. 2 July, 00:55
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    a) 0.804second

    b) 0.162m

    Explanation:

    In simple harmonic motion;

    Period T = 2π√m/k

    Where m is the mass of the object

    K is the force constant

    Given:

    M = 13.0kg

    K = 788N/m

    T = 2π√13/788

    T = 2π√0.0165

    T = 2π*0.128

    T = 0.804second

    Frequency is the reciprocal of the period. F = 1/T

    F = 1/0.804

    F = 1.244Hertz

    b) To get the amplitude x, we will use the relationship F = kx where F is the force exerted by the baby of mass 13kg

    x = F/k

    Since F = mg

    x = mg/k

    Assume g = 9.81m/s²

    x = (13*9.81) / 788

    x = 127.53/788

    x = 0.162m

    The minimum amplitude that she requires is 0.162m
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