An 0.90 kg object is attached to one end of a spring, and the system is set into

Question

An 0.90 kg object is attached to one end of a spring, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the drawing. With the aid of these data, determine the following values.

(a) amplitude A of the motion (answer should be in m).

(b) angular frequency ? (answer should be in rad/s).

(c) spring constant k (answer should be in N/m)

(d) speed of the object at t = 1.0 s (answer should be in m/s).

(e) magnitude of the object's acceleration at t = 1.0 s (answer should be in m/s^2)

Explanation / Answer

a) The amplitude is A = 0.08 m

b) The angular frequency w is 2 pi divided by the period (4 s).
w = (2 pi/ 4) = pi / 2 = 1.5708 rad / s

c) The spring constant is such that F = k A = M w^2 A
k = M w^2 = 2.22 N/m

d) At t = 1.0 s, the elongation is maximum and the speed is thus 0 m/s

e) The accelaration at that same time has a magnitude
w^2 A = 0.1974 m/s^2

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