When the displacement in shm is equal to 1/4 of the amplitude xm, what fraction of the total energy is (a) kinetic energy and (b) potential energy? (c) at what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy?

b)

Explanation:

Let the amplitude of SHM is given as A

so the total energy of SHM is given as

now we know that

a)

kinetic energy is given as

here

so now we have

now its fraction with respect to total energy is given as

b)

Potential energy is given as

so we have

so fraction of energy is given as

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.