Question

A spring is attached to a wall, and a 0.50 kg block is attached to the other end of the spring. The spring-block system sits on a frictionless surface so that the block is able to oscillate without losing energy. The spring constant of the spring is k = 25 N/m. The block is pushed so that it compresses the spring by 20 cm beyond its equilibrium position. The block is released from rest at exactly the same time as a stopwatch begins counting time.

I recommend including a plot of x-versus-t (a plot of displacement of the block versus time) as part of your answer, and use your sketch as part of the justification for your result.

a) At what time does the block first reach a point where it is halfway between its initial position (its position when the stopwatch began counting time), and the equilibrium position of the spring-mass system?

b) What is the position of the block 3.2 seconds after the stopwatch began counting time?

Answer 1

Displacement equation of block is

Equilibrium position of the block is taken as origin, initial position of block is

Angular frequency of block is

a)

When the block reaches halfway between initial position and equilibrium position ,

b)

At time

That is the block is to the left of equilibrium position.