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Find out the angular frequency of small ...

Find out the angular frequency of small oscillation about axis O

Text Solution

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The compression in spring (1) = `l theta`
and the extension in spring (2) = `l theta`
Net torque opposite to the mean position
=`- (2k theta ) t l - mg""(l)/(2)sin theta = tau_("net")`
`theta ` is small `implies sin theta = theta `
`tau_("net")= -Iomega^(2)theta=-(2k l theta ) l - mg ""(l)/(2) sin theta - tau_("net")`
`I = (ml^(2))/(3) " " implies omega= sqrt((3)/(2) ((4kl+mg))/(ml))`
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