Question

The drawing shows a top view of a frictionless horizontal surface, where there are two 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 at $x = 0$ $m$ if $m_{1} = 3$ $kg$ and $m_{2} = 27$ $kg$ . If time is $\frac{n \pi }{80}$ $\sec$ , fill $n$ in OMR sheet.

Answer 1

$\omega _{1} = \sqrt{\frac{1200}{3}} = 20$
$\omega _{2} = \sqrt{\frac{1200}{27}} = \frac{20}{3}$
$\omega _{1} = 3 \omega _{2}$
$t = \frac{\pi / 2}{\left(\omega \right)_{2}} = \frac{3 \pi }{2 \left(20\right)} = \frac{6 \pi }{80}$