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Mechanical Oscillations

Problem 4.83

A ball of mass \(m\) can perform undamped harmonic oscillations about the point \(x=0\) with natural frequency \(\omega_{0}\). At the moment \(t=0,\) when the ball was in equilibrium, a force \(F_{x}=F_{0} \cos \omega t\) coinciding with the \(x\) axis was applied to it. Find the law of forced oscillation \(x(t)\) for that ball.

Reveal Answer
x=F0/mω2−ω02(cos⁡ω0t−cos⁡ωt)x=\frac{F_{0} / m}{\omega^{2}-\omega_{0}^{2}}\left(\cos \omega_{0} t-\cos \omega t\right)
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