What is the equation for the kinetic energy of a pendulum at any point?

[velo city]

Homework Statement

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.

Homework Equations

θ = θ_maxcos(w*t) where w = √g/L

I = mL²

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

The Attempt at a Solution

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

\frac{dθ}{dt}=-θ_max*w*sin(w*t)

I have plugged that into find the kinetic energy but that's apparently not the right answer.

 

[velo city]

L is the length of the pendulum by the way.

 

[velo city]

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

KE = m*L²*θ_max²*w²*sin²(w*t)

 

[Uday]

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

 

[dauto]

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

 

[haruspex]

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.

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.