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A rod of mass m and length l hinged at o...


A rod of mass `m` and length `l` hinged at one end is connected by two springs of spring constant `k_1` and `k_2` so that it is horizontal at equilibrium What is the angular frequency of the system? (in `(rad)/(s)`) (Take `l=1m`,`b=(1)/(4)m`,`K_1=16(N)/(m)`,`K_2=61(N)/(m)`.

Text Solution

Verified by Experts


Applying torque equation about
`tau_0=l_0alpha`
`k_1bthetaxxcostheta+(k_2l_theta)/(theta)xxlcostheta=-(Id^2theta)/(dt^2)`
Here `I=(ml^2)/(3)`, and as `theta` is small `costheta=1`
`(ml^2d^2theta)/(3dt^2)+(k_1b^2+k_2l^2)theta=0`
Hence, `omega=sqrt((3k_1b^2+k_2l^2)/(ml))`
On substituting the values we get `omega=8(rad)/(s)`
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