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

Answer: 6

${\omega }_1=\sqrt{\frac{1200}{3}}=20$
${\omega }_2=\sqrt{\frac{1200}{27}}=\frac{20}{3}$
${\omega }_1=3{\omega }_2$
$t=\frac{\pi /2}{{\left(\omega \right)}_2}=\frac{3\pi }{2\left(20\right)}=\frac{6\pi }{80}$