Consider a harmonic oscillator at four different moments, labeled A, B, C, and D

Question

Consider a harmonic oscillator at four different moments, labeled A, B, C, and D, as shown in the figure below. Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. Answer the following questions:

A. If the k-constant of the spring is 15 N/m, the amplitude of oscillation is 22 cm, and attached mass is 750 grams then calculate the kinetic energy at point moment B.

B. At moment B, described in the previous question, calculate what fraction of the total energy of the system is kinetic energy.

Explanation / Answer

A.Since total energy = KE + PE and we only have enough information to find PE, we can work backwards by first finding the maximum PE (the PE when the spring is fully compressed) and then subtracting the PE at point B.

Maximum PE:

PEmax = 1/2kA2

PE at Point B:

PEB = 1/2k(A/2)2
PEB = 1/2k(A2/4)
PEB = 1/8k(A2)

Now find the difference between the PEs, and that difference must be KE since there is no friction:

KEB = PEmax

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