Question

A block is attached to a horizontal spring with a spring constant of 5.0 kg s?

2.

The block is displaced

0.5m from equilibrium and released (see the figure below). The block executes simple harmonic motion

with a period of 4.0 s .Assuming that the block is moving on a frictionless surface, and the spring is of

negligible mass.

a. Calculate the mass of the block?

b. Determine the velocity of the block 1.0 seconds after it is released?

The block is again displaced 0.5 m from its equilibrium position. At the instant it is released, it is

given an initial velocity of 1.0 m s?

1

in the direction toward its equilibrium position.

c. Find the amplitude (maximum displacement) of the block’s motion? Show your working.

Answer 1

a) The time period is

Hence the mass is

b) The position of the block is given by

where A = 0.5 m is the amplitude

The velocity is

At t = 1 s the velocity is

The magnitude of velocity is

c) For this problem

with

At t = 0

and

Therefore

This gives

Hence the amplitude is