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Physics HELP!

A 50-g mass is attached to a spring and undergoes simple harmonic motion. Its maximum acceleration is 15m/s2 and its maximum speed is 3.5m/s .

Determine the angular frequency.
Determine the spring constant.
Determine the amplitude of the motion.

how do I find these things?

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  1. 50 g = .050 kg = m

    sinusoidal motion kinematics:
    x = A sin wt
    v = Aw cos wt
    a = -Aw^2 sin wt = -w^2x

    givens:
    A w^2 = 15
    A w = 3.5
    so
    3.5 w = 15
    w = 15/3.5 radians /second first answer

    Newton #2
    F = -kx = m a
    so
    -k x = -m w^2 x
    or
    w^2 = k/m
    w = sqrt (k/m)
    15/3.5 = sqrt (k/.050)
    solve for k - second answer

    A = amplitude = 3.5/w third answer

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