Try this pendulum
A bob is attached to a pendulum of length 'L'. After giving some velocity it attains equilibrium angle for instant i.e.highest position. Now the length is made double , so calculate the extra velocity to be given in order to maintain same equilibrium angle.
initial velocity given , v=2m/s
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1 solution
If we move the pendulum to equilibrium angle A then we can say from conservation of energy principle that, mgL(1-cosA)=(1/2)mv^2 so we can see that (v^2) α L
so later v=(2^(1/2))*2 thus we get the required ans.2((2^.5)-1)