Find the period of small oscillation of the bob of mass m as shown in the figure. Mass of the rod is m.
2π√4m3k
(1) equilibrium x0=mgk rod will bend towards right.
(2) now displace the system x further
(3) note down the energy
12k(X+x0) − mgX + 12mv2 + 12lω2 =constant
spring Ball Ball Rod's
Potential Potential kinetic Rotational
Energy Energy Energy Energy
(4) Since total energy is constant dEdt=0
we get ω=√3k4m
T=2π√4m3k