A 0.79 -kg mass is attached to the end of a spring and set into oscillation on a

Question

A 0.79-kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing.

Determine the following.

A 0.79-kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing. Determine the following. amplitude A of the motion spring constant k speed of the object at t = 2.0 s magnitude of the object's acceleration at t = 2.0 s

Explanation / Answer

Here

Amplitude = 0.10 m

Time period = 8 sec

T = 2pi*sqrt(m/k)

8 = 2pi*sqrt(0.79/k)

k = 0.487 N/m

w = sqrt(k/m)

= sqrt(0.487/0.79)

= 0.785 rad/sec

Here

v = wACos(wt)

= 0.785*0.10*Cos(0.785*2)

= 0.785*0.10*Cos(90 degree)

= 0 m/sec

Acceleration =- w^2ASin(wt)

= 0.785^2*0.10*Sin(0.785*2)

= 0.0616 m/sec^2

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