A square hinged -structure `(ABCD)` is formed with four massless rods which lie 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 along line `BD` and released to perform SHM. The time period of SHM is `pisqrt((nm)/k)`. Find n

Answer

4

Explanation

`OE=x`
`FG=sqrt(2)a+2y`
From the property of rhombus, we can write
`(a/(sqrt(2))+y)^(2)+(a/(sqrt(2))-x/2)^(2)=a^(2)`
Neglecting `x^(2)` and `y^(2)`, we have `y=x/2`
Using COME, we can write
`(mv^(2))/2+k/2(x)^(2)=E=` constant
`impliesT=pisqrt((4m)/k)`