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.

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. <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-5wfu3vpkxu1mz38h.jpg" /> (A) 2π √(2 M/3 K) (B) 2π √(M/6 K) (C) π √(M/3 K) (D) None of the above.

Tardigrade Admin · Accepted Answer

Torque about B , -Kbx=(2 M b2 α /3) -Kbx=(2 M b2 a/3 b) ⇒ a=-(3/2)(K x/M) ⇒ ω 2=(3 K/2 M) T=(2 π /ω )=2π √(2 M/3 K) .

Q. 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.

$2 π \frac{2 M}{3 K}$

$2 π \frac{M}{6 K}$

$π \frac{M}{3 K}$

None of the above.

Torque about $B$ ,
$- K b x = \frac{2 M b ^{2} α}{3}$
$- K b x = \frac{2 M b ^{2} a}{3 b}$
$\Rightarrow a = - \frac{3}{2} \frac{K x}{M}$
$\Rightarrow ω^{2} = \frac{3 K}{2 M}$
$T = \frac{2 π}{ω} = 2 π \frac{2 M}{3 K}$ .

Q. 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.

2π3K2M​​

2π6KM​​

π3KM​​