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Problem: An object attached to a spring experiences simple harmonic motion (define the potential energy of the object + spring system to be zero when it is in equilibrium). (a) When the displacement of the object is one-half the maximum amplitude A, what fraction of the total energy is kinetic and what fraction is potential? (b) At what displacement x is the total energy half kinetic and half potential?

FREE Expert Solution

The expression for the total energy of a simple harmonic oscillator is:

E=12kA2=12mvmax2=12kx2+12mv2 

We are told that at the equilibrium position, U = (1/2)kx2 = 0

Consequently, U = 0 when K = Kmax (Equilibrium position) and K = 0 when U = Umax (Maximum displacement).

K is maximum at the equilibrium position where x = 0 and v = vmax.

U is maximum at the turning points where v = 0 and x = A.

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Problem Details

An object attached to a spring experiences simple harmonic motion (define the potential energy of the object + spring system to be zero when it is in equilibrium). 

(a) When the displacement of the object is one-half the maximum amplitude A, what fraction of the total energy is kinetic and what fraction is potential? 

(b) At what displacement x is the total energy half kinetic and half potential?

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