Question

A uniform thin rod has a mass 1 kg and carries a mass 2.5 kg at B. The rod is hinged at A and is maintained in the horizontal position by a spring having a spring constant 18 kNm^–1 at C as shown in figure. The angular frequency of oscillation is nearly –

• A. 10 rad/s
• B. 20 rad/s
• C. 40 rad/s
• D. 80 rad/s

Answer 1

Answer: (C)

40 rad/s

Answer 2

Let x₀­ be the extention in equilibrium

mgl = kx₀l

After slightly displacing

mgl – k (x + x₀) = I_Aa

I_A = ml² + $\frac { \mathrm { m } _ { \mathrm { rod } } \ell ^ { 2 } } { 3 }$ = 1.02 kgm²

Solving, a = $\frac { - \mathrm { k } \ell } { \mathrm { I } _ { \mathrm { A } } }$ x

w = $\sqrt { \frac { \mathrm { k } \ell } { 2 \mathrm { I } _ { \mathrm { A } } } }$