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**[SOLVED] Potential energy of a pendulum when the angle is small**

**1. The problem statement, all variables and given/known data**

When a simple pendulum makes an angle with the vertical, its speed is v. (a) Calculate the total mechanical energy of the pendulum as a function of v and [tex]\theta[/tex]. (b) Show that when [tex]\theta[/tex] is small, the potential energy can be expressed as [tex]\frac{1}{2}mgL\theta^2=\frac{1}{2}m\omega^2s^2[/tex] (Hint: In part (b), approximate [tex]cos\theta[/tex] by [tex]cos\theta\approx1-\frac{\theta^2}{2}[/tex]

Note: s is the displacement of the pendulum.

**3. The attempt at a solution**

OK...I solved part (a) with no problem, I was able to obtain the correct answer by adding the kinetic and potential energy. My problem lies with part (b). I am really confused by what exactly I must do, and where the squares of the angles are coming from. I know I somehow have to find a way to connect all of the variables together, but I can't see where the variables in the final equation would come from. I would appreciate just a tiny push in the right direction to coming up with the right answer.