Asimple harmonic oscillator of amplitude a has a total energy e.

a) determine the kinetic energy when the position is one-third the amplitude. (use any variable or symbol stated above as necessary.) k =
b) determine the potential energy when the position is one-third the amplitude. (use any variable or symbol stated above as necessary.)

a)

b)

Explanation:

The law of conservation of mechanical energy states that total mechanical energy remains constant during oscillation. Mechanical energy is defined as the sum of kinetic energy and potential energy:

a) The position is one-third the amplitude. So, we have . Replacing and solving for K

b) The potential energy is defined as:

Replacing: