Question

An object having mass m is attached to a spring of force constant k oscillates with simple harmonic motion. The total mechanical energy of the system is E and the maximum displacement from equilibrium is A. What is the system's potential energy when its kinetic energy is equal to 3/4E?

Answer 1

The system's potential energy is
`(kA^(2) )/(8)`

Step-by-step explanation:

The total mechanical energy of the system is E which the sum of the potential energy and the kinetic energy.

The total energy of a simple harmonic oscillator is given as E =
`(1)/(2)kA^(2)`.

The system's kinetic energy is given as
`(3)/(4) E`

Total system Energy (E) = Potential Energy (P) + Kinetic Energy (K)

E = P+K

P = E - K

P =
`(1)/(2)kA^(2) - (3)/(4)E`

P =
`(1)/(2) kA^(2) - (3)/(8) kA^(2)` =
`(kA^(2) )/(8)`

Potential Energy (P) of the system =
`(kA^(2) )/(8)`