An object of mass m is attached to a spring having force constant k. The object

Question

An object of mass m is attached to a spring having force constant k.

            The object oscillates with simple harmonic motion.

            Its maximum displacement from equilibrium is A.

            What is the total mechanical energy of the spring/mass system when

            The object is located at

            (a)        x = +A

            (b)       x = %u2013A

            (c)        x = 0

            Also, when the object is located at x = +A/2,

            (d)       what is the potential energy of the system?

            (e)        what is the kinetic energy of the system?

Explanation / Answer

for a, b,c all cases total energy of system is always consatnt and is equal to 1/2KA^2

d) potential energy = 1/2kx^2 here x=A/2 so PE= 1/8KA^2 and KE= total - PE = 3/8kA^2

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