an object-spring system moving with simple harmonic motion has an amplitude A. a

Question

an object-spring system moving with simple harmonic motion has an amplitude A. a) what is the total energy of the system in terms of k and A only? b) suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write an equation describing this situation, using only the variables for mass m, velocity v, spring constant k, and position x. c) using the results of parts a and b, and the conservation of energy equation, find the positions x of the object when its kinetic energy equals twice the potential energy stored in the spring (this answer should be in terms of A only)

Explanation / Answer

a) total energy of the system = k A^2 / 2

b) P.E+k.E=3P.E   as KE = 2PE

This gives P.E=kA^2/6=kx^2/2

c) If kinetic energy = 2 x potential energy, the potential energy at that point = 1/3 the total energy
in the system, which is (k A^2 / 2). Since the energy stored in the spring is proportional to the
square of the extension, it will be 1/3 of the total at x = A / sqrt(3).

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