A mass of 0.50 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.50 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.46 m)cos[(18 rad/s)t]. Determine the following.

(a) amplitude of oscillation for the oscillating mass m

(b) force constant for the spring N/m

(c) position of the mass after it has been oscillating for one half a period m

(d) position of the mass one-third of a period after it has been released m

(e) time it takes the mass to get to the position x = 0.10 m after it has been released s

Explanation / Answer

a) Amplitude A = 0.46 m

b) k = m w2 = 0.50 * 182= 162 N/m

c) T = 2 pi / w

x = 0.46 * cos pi = -0.46 m

d) x = -0.23 m

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