A massless rod rigidly fixed at O. A sting carrying a mass m at one end is attached to point A on the rod so that `OA = a`. At another point `B(OB = b)` of the rod, a horizontal spring of force constant k is attached as shown. Find the period of small vertical oscillations of mass m around its euqilibrium position.

Answer

A, B

Explanation

From energy equation

`1/2 mv^(2) + 1/2k(x/ab)^(2) = E`
`rArr ma + (kb^(2))/(a^(2)) x = 0 rArr t = 2pi(a)/(b) sqrt((m)/(k))`