An object- spring system moving with simple harmonic mot ion has an amplitude A.

Question

An object- spring system moving with simple harmonic mot ion has an amplitude A. What is the total energy of the system in terms of k and A only? E = Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Writ e an equation describing this situation, using only the variables for the mass m, velocity v, spring constant k, and posit ion x. (Do this on paper. Your instructor may ask you to turn in this work.) Using the results of parts (a) and (b) and the conservation of energy equation, find the posit ions x of the object when its kinetic energy equals twice the potential energy stored in the spring. (The answer should in terms of A only.)

Explanation / Answer

a) E = (1/2)kA2

b) KE is twice the potential energy

(1/2)mv2 = 2*(1/2)kx2

mv2 = 2kx2

c)

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