The drawing shows a top view of a frictionless horizontal surface, where there are two indentical springs with particles of mass $m_1$ and $m_2$ attached to them. Each spring has a spring constant of $1200\ N/m.$ The particles are pulled to the right and then released from the positions shown in the drawing. How much time passes before the particles are again side by side for the first time if $m_1 = 3.0\ kg$ and $m_2 = 27 \,kg \,?$
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$w_{1}=\sqrt{\frac{k}{m_{1}}}=\sqrt{\frac{1200}{3}}=20 \mathrm{rad} / \mathrm{s}$
$\omega_{2}=\sqrt{\frac{1200}{27}}=\frac{20}{3} \operatorname{rad} / s$
$\pi-\theta=\frac{20}{3} t$
$\pi+\theta=20 t$
$2 \pi=\left(20+\frac{20}{3}\right) t$
$t=\frac{6 \pi}{80}=\frac{3 \pi}{40} \mathrm{sec}$
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