Question

A spring is stretched from x=0 to x=d, where x=0 is the equilibrium position of the spring. It is then compressed from x=0 to x=−d. What can be said about the energy required to stretch or compress the spring?

Answer 1

Answer:

The energy stored in the later case is equal to the energy stored in the former  case of the spring.

Explanation:

For a spring we have the expression of kinetic energy as:

$\rm KE=\frac{1}{2} k.x^2$

where:

k= elastic constant of the spring

x= length of deflection of the spring from the mean position

Here we are given two cases:

CASE:1

x=d

$\therefore KE_1=\frac{1}{2} k.(d)^2$

CASE:2

x=-d

$\therefore KE_2=\frac{1}{2} k.(-d)^2$

$\therefore KE_2=\frac{1}{2} k.d^2$

So, we get

$KE_1=KE_2$

Just the difference in the two cases is that there is deflection of the spring in the opposite direction.