Question

A 215 g object is attached to a spring that has a force constant of 72.5 N/m. The object is pulled 7.75

cm to the right of equilibrium and released from rest to slide on a horizontal, frictionless table.

Calculate the maximum speed of the object.

maximum speed:

m/s

Find the locations of the object when its velocity is one-third of the maximum speed. Treat the equilibrium position as zero, positions to the right as positive, and positions to the left as negative.

position:

cm

position:

cm

Answer 1

Lets, we know that  

Where.

a = the amplitude of oscillation,

v = the velocity of the mass,

x= the displacement from the equilibrium point.

k = the force constant =72.5 N/m

and m=  is the mass attached =0.215

At the equilibrium position, the velocity will be maximum and the total energy will be equal to kinetic energy. Then, we can write

ka² =mv²

  

  

The maximum speed is 1.423 m/s

When the velocity is one third, we have

  Then, the position is,

  

Where v replace by

So.

  

Positions to the right as positive =+0.073 m

and  positions to the left as negative = -0.073 m

±0.073 m is correct answer