An object of mass m attached to a spring of force constant k oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E. Part A What is the system's potential energy when its kinetic energy is equal to 34E

The correct question is;

An object of mass m attached to a spring of force constant K oscillates with simple harmonic motion. The maximum displacement from equilibrium is A and the total mechanical energy of the system is E.

What is the system's potential energy when its kinetic energy is equal to ¾E?

P.E = ⅛KA²

Explanation:

From conservation of energy, the total energy in the system is given as the sum of potential and kinetic energy.

Thus,

Total Energy; E = K.E.+P.E.

In simple harmonic motion, the total energy is given by;

E = ½KA²

We are told that kinetic energy is ¾E.

Thus, ½KA² = ¾(½KA²) + P.E

P.E = ½KA² - ⅜KA²

P.E = ⅛KA²

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