Question

1)a particle is executing shm of amplitude A.what fraction of total energy is kinetic energy when displacement is 1/2 the amplitude.what is the potential energy at that instant??

2)find ratio of a SHM at a distance of (root)3/2 of its amplitude to that of the extreme position.

Answer 1

The total energy is given as

E = PE + KE = (1/2)kA²

now,

PE = (1/2)kx²

here

x = A/2

thus,

PE = (1/2)k.(A/2)²

= (1/8)kA²

so,

PE = (1/4).[(1/2)kA²]

or

PE = E/4

and so, kinetic energy

KE = E - PE = E - E/4

so,

KE = (3/4).E