A student attaches a block of mass M to a vertical spring so that the block-spring system will oscillate if the block-spring system is released from rest at a vertical distance D below the system’s equilibrium position. The student measures the period of oscillation for the system to be P. What is the maximum spring potential energy of the system Us in terms of D, M, and P ?

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answer: the potential energy decreases from 379 j to 243 j

explanation:

for the law of conservation of energy, the total energy in a system must be conserved. the total energy of the system is given by the sum of kinetic (k) and potential (u) energy:

e = k + u

the total energy is e=675 j, and this does not change.

initially, the kinetic energy is k=296 j, so the potential energy is

at the end, the kinetic energy is k=432 j, so the potential energy is

so, we see that the potential energy has decreased from 379 j to 243 j.