I need help figuring out this problem. An object of mass m attached to a spring

Question

I need help figuring out this problem. An object of mass m attached to a spring of forceconstant k oscillates with simple harmonic motion. Themaximum displacement from equilibrium is A and the totalmechanical energy of the system is E. What is the system's potential energy when its kinetic energyis equal to 3/4E? Options: kA2, kA2/2, kA2/4,kA2/8 Thanks! I need help figuring out this problem. An object of mass m attached to a spring of forceconstant k oscillates with simple harmonic motion. Themaximum displacement from equilibrium is A and the totalmechanical energy of the system is E. What is the system's potential energy when its kinetic energyis equal to 3/4E? Options: kA2, kA2/2, kA2/4,kA2/8 Thanks!

Explanation / Answer

Total energy= PEmax on the spring = KEmax of the oject Total Energy= KE+PE at v or x not maximum. Using the second line E= 3/4 E + PE PE = 1/4 E PEmax =E = 1/2 kA^2 PE=E/4 = (1/2)kA^2 / 4= kA^2/8

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