A rod of length `l` and mass `m`, pivoted at one end, is held by a spring at its mid – point and a spring at far end. The spring have spring constant `k`. Find the frequency of small oscillations about the equilibrium position.
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Correct Answer – A::B::D
Restoring torque
`tau = – (kl theta)l – (k(l)/(2)theta)(l)/(2) = – (5)/(4)kl^(2)theta`
Now, `((ml^(2))/(3))alpha = – ((5)/(4)kl^(2))theta`
`f = (1)/(2pi)sqrt|(alpha)/(theta)| = (1)/(2pi)sqrt((15k)/(4m))`