A pendulum of period 2s is released from rest at an inclination of 5 degrees to the downward vertical. What is its angular velocity when it reaches the vertical?

$\displaystyle \tau=\frac{2\pi}{\omega}$

$\displaystyle \omega=\frac{2\pi}{2}$

$\displaystyle \omega=\pi$

however the answer in book is 15.7degrees/sec

Further,

When it first returns to the starting point, it is given an impulsive blow towards the vertical that increases the amplitude of swing to 10degrees. Find its subsequent angular postion as a function of time.

the pendulum has a restoring force of :

$\displaystyle F=-mgsin\theta$

$\displaystyle m\ddot{x}=-mgsin\theta$

i realise the acceleration is centripetal so $\displaystyle \ddot{x}=r(\omega)^2$

also i think you should go down the the integration with respect to time and use angular measurements instead of linear. This is where im stuck.