A 100-g object is fixed to the end of a spring that has a spring constant of 15.

Question

A 100-g object is fixed to the end of a spring that has a spring constant of 15.0 N/m. The object is displaced 15.0 cm to the right and released from rest at t = 0 to slide on a horizontal, frictionless table.

1) Calculate the first time when the object is at the equilibrium position. (Express your answer to three significant figures.)

2) What is the first time when the object is 10.0 cm to the left of equilibrium? (Express your answer to three significant figures.)

3) What is the first time that the object is 5.00 cm to the right of equilibrium, moving toward the left? (Express your answer to three significant figures.)

Explanation / Answer

1. Time period, T= 2* pi* (m/k) = 2* 3.14* ( 0.1/15)= 0.51276 s

Time taken to reach equilibrium position at first time, t= T/4= 0.1282 s

2. As spring position is given by

x= A cos(wt)      ....(i)

w= 2*pi/T= 2*3.14/ 0.51276= 12.247 rad/s

A= 0.15 m

x= 0.1

Putting in ..(i)

-0.1= 0.15 cos(12.247*t)

t= 0.1878 s

3. 0.05 = 0.15 cos(12.247t)

t= 0.1005 s

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