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The Fundamental Equation of Dynamics

Problem 1.99

At the moment \(t=0\) a particle of mass \(m\) starts moving due to a force \(F=F_{0} \cos \omega t,\) where \(F_{0}\) and \(\omega\) are constants. How long will it be moving until it stops for the first time? What distance will it traverse during that time? What is the maximum velocity of the particle over this distance?

Reveal Answer
 1.99. t=π/ω;s=2F0/mω2vmax⁡=F0/mω.\begin{aligned} &\text { 1.99. } \quad t=\pi / \omega ; \quad s=2 F_{0} / m \omega^{2}\\ &v_{\max }=F_{0} / m \omega . \end{aligned}
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