Problem 5: Consider a 1D simple harmonic oscillator (without damping). (a) Compute the time averages of the kinetic and potential energies over one cycle, and show that they are equal. Why does this make sense? (b) Show that the space averages of the kinetic and potential energies are (T)₂ = KA² KA² and (U),= KA². Why is this a reasonable result?
Problem 5: Consider a 1D simple harmonic oscillator (without damping). (a) Compute the time averages of the kinetic and potential energies over one cycle, and show that they are equal. Why does this make sense? (b) Show that the space averages of the kinetic and potential energies are (T)₂ = KA² KA² and (U),= KA². Why is this a reasonable result?
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Transcribed Image Text:Problem 5: Consider a 1D simple harmonic oscillator (without damping). (a) Compute
the time averages of the kinetic and potential energies over one cycle, and show that they
are equal. Why does this make sense? (b) Show that the space averages of the kinetic and
potential energies are
(T)₂ = k1²
KA² and (U),= KA².
Why is this a reasonable result?
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