The block in the figure below lies on a horizontal frictionless
surface and is attached to the free end of the spring, with a spring
constant of 35 N/m. Initially, the spring is at its relaxed length and
the block is stationary at position x = 0. Then an applied force with
a constant magnitude of 2.7 N pulls the block in the positive
direction of the x axis, stretching the spring until the block stops.
Assume that the stopping point is reached
MY questions is how do you find the maximum kinetic energy of the spring during the blocks displacement?
You know that the restoring force of the spring is F=-kx where k is the spring constant and x is the displacement of the spring (negative because it acts in the direction opposite to the displacement x of the spring).
You are given an applied force of 2.7N that causes displacement in the positive x direction.
Using a free-body diagram you should find the net force on the block. You should see that there is no net force in the y direction and that along the x direction, you have the spring force and the applied force acting in opposite directions. The magnitudes of the spring force and the applied force are equal at the stopping point.
Now you can find the displacement x.
Force applied over a distance results in work. Work is a form of energy. Do you know the equation for work?