Science

A body weighing 150 N, moves with simple harmonic motion. The velocity and
acceleration of the body when it is 200 mm from the centre of oscillation, are 5 m/s
and 20 m/s2 respectively.Determine (a) amplitude of motion ,no. of vibrations per minute, Periodic time and angular velocity

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  1. mass = 150/g or about 15 kg but who needs it?

    x = A sin w t
    v = Aw cos wt
    a = -Aw^2 sin wt = -w^2 x
    =============================
    when
    x = .2 = A sin w t
    v = 5 = Aw cos w t
    a = +20=+Aw^2 sin w t = +w^2x
    ===============================
    so
    w^2 x = w^2(.2) = 20
    w^2 = 200/2 = 100
    w = 10 radians/sec

    now rewrite
    .2 = A sin 10 t
    5 = 10 A cos 10t
    20 = 100A sin 10t

    .2 = A sin 10 t
    .5 = A cos 10 t

    .04 = A^2 sin^2 10 t
    .25 = A^2 cos^2 10 t

    .04/A^2 + .25/A^2 = sin^2+cos^2 = 1

    A^2 = .29

    I guess you can take it from there
    remember w = 2 pi f = 10
    so f = 5/pi

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