Math Solutions

[See Steps] Show that if l_1=l_2=1, and if ω_1=2 rad / s and ω_2=3 rad / s, then the parametric equations of motion are x= cos 2 t+ cos 5 t

Question: Show that if \(l_{1}=l_{2}=1\), and if \(\omega_{1}=2 \mathrm{rad} / \mathrm{s}\) and \(\omega_{2}=3 \mathrm{rad} / \mathrm{s}\), then the parametric equations of motion are

\[\begin{aligned} &x=\cos 2 t+\cos 5 t \\ &y=\sin 2 t+\sin 5 t \end{aligned}\]

Use a graphing utility to show that the curve traced by the end effector over the time interval \(0 \leq t \leq 2 \pi\) is as shown in Figure 4 . This would be the painting pattern of Robin's paint sprayer.

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