Concept Simulation 10.3 illustrates the concepts pertinent to this problem. A 0.

Question

Concept Simulation 10.3 illustrates the concepts pertinent to this problem. A 0.94-kg object is attached to one end of a spring, as in the first drawing, and the system is set into simple harmonic motion. The displacement x of the object as a function of time is shown in the second drawing. With the aid of these data, determine (a) the amplitude A of the motion, (b) the angular frequency , (c) the spring constant k, (d) the speed of the object at t = 1.0 s, and (e) the magnitude of the object's acceleration at t = 1.0 s.

Explanation / Answer

a) A = 0.080 m

b) Angular frequency, = 2/T = 2/4 = 1.57 rad/s

c) For SHM of spring mass system, 2 = k/m

=> k = m2 = 0.94 * 1.572 = 2.32 N/m

d) Equation of motion is, x = 0.080 sin(1.57t)

So, v = dx/dt = (0.080 * 1.57) cos(1.57t)

At t = 1.0 s, v = (0.080 * 1.57) cos1.57 = 0

e) a = dv/dt = -(0.080 * 1.572) sin(1.57t)

At t = 1.0 s, a = -(0.080 * 1.572) sin1.57 = -0.20 m/s2

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