In the Figure shown, a cord is attached between a 2 kg block and a spring with force constant k = 20 Nm-1. The other end of the spring is attached to the wall, and the cord is placed over a pulley (I = 0.60MR2) of mass 5 kg and radius 0.5 m. Assuming no slipping occurs, what is the angular frequency of the oscillations when the body is set into motion?

m = mass of block = 2 kgIn equilibrium, kr0 = mg                  ……....(1)When displaced further by x,          E=12kv2+12Iω2−mgx+12kx+x02⇒ E=12mv2+120.6MR2v3R2−mgx+12kx+x02⇒ E=12(m+0.6M)v2−mgx+12kx+x02Since, E = constant⇒ dEdt=0⇒ v(m+0.6M)dvdt−mgdxdt+kx0+xdxdt=0Substituting dxdt=v,dvdt=a and kx0=mgWe get (m+0.6M)a=−kx⇒ f=12πax=12πkm+0.6M⇒ ω=2πf=ux=km+0.6M⇒ ω=202+(0.6)(5)=205=4rads−1