An 0.65 kg object is attached to one end of a spring, and the system is set into

Question

An 0.65 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
m

(b) angular frequency ?
rad/s

(c) spring constant k
N/m

(d) speed of the object at t = 1.0 s
m/s

(e) magnitude of the object's acceleration at t = 1.0 s
m/s2

An 0.65 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 m (b) angular frequency ? rad/s (c) spring constant k N/m (d) speed of the object at t = 1.0 s m/s (e) magnitude of the object's acceleration at t = 1.0 s m/s^2

Explanation / Answer

amplitude A of the motion = 0.080 m
angular frequency w = 2pi/T = pi/2 Hz
but w^2 = k/m
so k = mw^2
the velocity v is the slope of the tangent line of the x ~ t curve, so v = 0 at t = 1.0 s.
the acceleration a = -w^2*x, at t = 1.0 s, x = A, so the magnitude of the acceleration at t = 1.0 s is w^2*A

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