A light wooden rod fixed at one end is kept horizontal. A load of m = 0.4 kg tied to the free end of the rod causes that end to be depressed by δ = 2.5 cm. If this load is set into up and down vibration, will it oscillate? Find its angular frequency (rad/s) of oscillation. Take g = 10 m/s2.

Due to elasticity in rod it sags by weight of load. If its Young modulus of elasticity is Y for equilibrium of system, thenY=F/Aδ/l [where A is area of cross section and l is its length]Rearranging above equation, MgA=Yδl ……(i)If load is depressed by x we use F−Mg=Ma …….(ii)where Y=F/A(δ+x)/l⇒ F=YAl(δ+x)From (ii) we use, YAl(δ+x)−Mg=MaIt means, a=YAlM⋅xFrom (i) we use for restoring accelerating, a=−gδxThis shows that load executes SHM.Comparing with, a=−ω2xWe get ω=gδ=102.5×10−2=20 rad/s