00:01
In this problem, we have been given the variation of the spring force with respect to the displacement, and this is a nonlinear spring.
00:09
So the relation between force and displacement is given as f is equal to minus 3k x square.
00:16
So basically the force varies with the displacement according to this equation, provided that x is the displacement with respect to the equilibrium position of the block that's connected to the spring.
00:28
So here we need to determine the potential energy that gets stored in the spring, provided that x is the displacement with respect to the equilibrium position.
00:40
So the work that will be done when the block is compressed, let's say by distance x, so small amount of potential energy stored, or let's just figure out the work done first.
00:51
So that will be force times small displacement.
00:54
And let's consider this as the spring.
00:56
And if we are providing the force, and this force is in the direction of the displacement, so this comes out to be approximately minus 3kx square.
01:11
That's the value we put for f times dx...