Question

A uniform square plate of mass $m$ is supported on a horizontal plane by a vertical pin at $B$ and is attached at $A$ to a spring of constant $k$ . If corner $A$ is given a small displacement and released, determine the period of the resulting motion.

• A. $2\pi \sqrt{\frac{2 M}{3 K}}$
• B. $2\pi \sqrt{\frac{M}{6 K}}$
• C. $\pi \sqrt{\frac{M}{3 K}}$
• D. None of the above.

Answer 1

Answer: (A)

Torque about $B$ ,
$-Kbx=\frac{2 M b^{2} \alpha }{3}$
$-Kbx=\frac{2 M b^{2} a}{3 b}$
$\Rightarrow a=-\frac{3}{2}\frac{K x}{M}$
$\Rightarrow \omega ^{2}=\frac{3 K}{2 M}$
$T=\frac{2 \pi }{\omega }=2\pi \sqrt{\frac{2 M}{3 K}}$ .