The maximum angular displacement of a simple pendulum of length l is $\theta$. Find the maximum kinetic energy of a bob of mass m.

When pendulum passes through mean position, then its kinetic energy will be maximum.

So, by conservation of mechanical energy from A to B

$\text{ M. }{\mathrm{E}}_{\mathrm{A}}=\text{ M. }{\mathrm{E}}_{\mathrm{B}}$

i.e. mgh = (K.E)_max.  …….. (i)

By diagram, $\mathrm{h}=1(1-\cos \theta )$ …..(ii)

By equations (i) and (ii), we get

$(\mathrm{K}.\text{ E. }{)}_{max}=\mathrm{mgl}(1-\cos \theta )$