University Physics III · Oscillations, damping, and resonance
Prove conservation of ideal oscillator energy
Problem
Let $x(t)$ satisfy $m\ddot x+kx=0$ with $m,k>0$. Prove directly that $E(t)=\tfrac12m\dot x^2+\tfrac12kx^2$ is constant, and explain why this proof fails unchanged when a term $b\dot x$ is added.
Hint
Differentiate $E(t)$ using the chain rule.
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