When the displacement of a mass on a spring is 1/2a the half of the amplitude, what fraction of the mechanical energy is kinetic energy?

Explanation:

As we know that the total mechanical energy of the object which is executing SHM is given by

here we know that

A = amplitude of SHM

K = spring constant

now we know that total mechanical energy of the spring is always constant so here we can say

kinetic energy + Potential energy = total mechanical energy

we know that potential energy of the spring at any given distance is

at given position x = A/2

now we have

now ratio of kinetic energy and total mechanical energy will be given as

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered