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  4. A rectangular plate of mass M, sides l1 and l2 is suspended from a ceiling by two parallel strings of length l3 each as shown in figure. The plate is displaced slightly in its plane keeping the strings tight. The angular frequency of its SHM is ω. Find the value of 2 ω2 in SI units. [. Take .: M=10 kg , l1=0.8 m , l2=0.2 m , l3=0.4 m ]

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Q. A rectangular plate of mass $M$, sides $l_{1}$ and $l_{2}$ is suspended from a ceiling by two parallel strings of length $l_{3}$ each as shown in figure. The plate is displaced slightly in its plane keeping the strings tight. The angular frequency of its SHM is $\omega$. Find the value of $2\, \omega^{2}$ in $SI$ units.
$\left[\right.$ Take $\left.: M=10\, kg , l_{1}=0.8\, m , l_{2}=0.2\, m , l_{3}=0.4\, m \right]$Physics Question Image

Oscillations

Solution:

The motion of the plate is translational motion.
image
For small angle $\theta, 2 T=m g$
$2 T \sin \theta=m a$
$\therefore m g\left(\frac{-x}{l}\right)=m a$
$\Rightarrow a=-\frac{g}{l} x=-\omega^{2} x$
$\Rightarrow \omega=\sqrt{\frac{g}{l}}$