A square hinged-structure (ABCD) is formed with four massless rods which lies on the smooth horizontal table. The hinge-D of structure is fixed with table and hinge A, hinge-B and hinge-C are free to move on the table. A point mass m is attached at hinge-B, and an ideal spring of stiffness k is connected between hinge-A and hinge-C as shown in the figure. System is in equilibrium. The mass m is slightly displaced along line BD and released to perform SHM. The time period of SHM is $π \sqrt{\frac{n m}{k}}$ . Find

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answer is 4.

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Detailed Solution

OE=x
$F G = \sqrt{2} a + 2 y$
From the property of rhombus, we can write
${(\frac{a}{\sqrt{2}} + y)}^{2} + {(\frac{a}{\sqrt{2}} - \frac{x}{2})}^{2} = a^{2}$
Neglecting $x^{2} a n d y^{2}$ , we have
Using COME, we can write
$\frac{m v^{2}}{2} + \frac{k}{2} {(x)}^{2} = E = c o n s \tan t \Rightarrow T = π \sqrt{\frac{4 m}{k}}$