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 0.69-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 w, (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

Here ,

mass of object , m = 0.69 Kg

a) from the graph ,

amplitude = 0.080 m

the amplitude A is the motion is 0.080 m

b)

angular frequency , f = 1/T

f = 1/4 = 0.25 Hz

w = f/2pi

w = 0.25/2pi

w = 0.0397 rad/s

the angular freqeuncy is 0.0397 rad/s

c)

spring constnat is k

w = sqrt(k/m )

0.0397 = sqrt(k/.69)

k = 1.093 *10^-3 N/m

the spring constant is 1.093 *10^-3 N/m

d)

as the particle is at the maximum position ,

the velocity at t= 1 will be ZERO

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