A thin uniform Plank of length 21 and mass m rests on two id

A thin uniform Plank of length 21 and mass m rests on two identical springs each with a spring constant k. The plank in its equilibrium position is horizontal, emu the normal mode frequencies of small vertical oscillations of the planR. ( The moment of inertia of the plank through its mass centre about a horizontal axis perpendicular to its length is I - 1/3 ml^2 )

Solution

this combination of springs is in parallel so equivalent spring constant

Keq = K+K = 2K

frequency

f = (1/2pi)sqrt(Keq/m)

f = 1/2pi sqrt(2K/m)