Find the period of each pendulum when it is pulled 20 ° to the right and then re

Question

Find the period of each pendulum when it is pulled 20 ° to the right and then released.

(a) a rod has a mass M and a length L (Use any variable or symbol stated above along with the following as necessary: g.)
T =

(b) a rod has a mass 2M and a length L (Use any variable or symbol stated above along with the following as necessary: g.)
T =

(c) a mass M is attached to a massless string of a length L (Use any variable or symbol stated above along with the following as necessary: g.)
T =

(d) a mass M is attached to a massless string of length

Explanation / Answer

a)ml^2/3 *w^2theta=mgl/2 *theta

or w=(3g/2l)^1/2

so T=2pi/w

=2pi*(2l/3g)^0.5

b)2ml^2/3 *w^2theta=2mgl/2 *theta

or w=(3g/2l)^1/2

so T=2pi/w

=2pi*(2l/3g)^0.5

c)mgltheta=ml^2*w^2theta

or w=(g/l)^0.5

so,

T=2pi/w

=2pi*(l/g)^0.5

d)2mgltheta=4ml^2*w^2theta

or w=(2g/l)^0.5

so,

T=2pi/w

=2pi*(l/2g)^0.5

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