# Kinetic Energy of a Pendulum

1. May 31, 2014

### velo city

1. The problem statement, all variables and given/known data
I want to find the equation of the kinetic energy of a pendulum at any point. I know the initial angle it is released from but I am having trouble finding the velocity at any point to be able to find the kinetic energy at any point.

2. Relevant equations

θ = θmaxcos(w*t) where w = √g/L

I = mL2

KErotational=(1/2) *I($\frac{dθ}{dt}$)2

3. The attempt at a solution

I differentiated the θ function with respect to time to get dθ/dt

$\frac{dθ}{dt}$=-θmax*w*sin(w*t)

I have plugged that in to find the kinetic energy but thats apparently not the right answer.

2. May 31, 2014

### velo city

L is the length of the pendulum by the way.

3. May 31, 2014

### velo city

After plugging In I have found that the kinetic energy at any point is:

KE = m*L2max2*w2*sin2(w*t)

4. Jun 1, 2014

### Uday

may i know how u conclude it to be the wrong answer ?

5. Jun 1, 2014

### dauto

There is nothing wrong with your formula. why do you say it's wrong?

6. Jun 1, 2014

### haruspex

It depends whether you want the exact equation or the SHM approximation for small angle displacements (which is what you posted).
For the question as stated, you could provide the exact answer. Maybe that's what's wanted here.