Physics Van 3-site Navigational Menu

Physics Van Navigational Menu

Q & A: Equations for an oscillating pendulum

Learn more physics!

Most recent answer: 07/08/2014
Q:
For a pendulum, what does speed equal at h=max at both sides of the arc pathway? I get that velocity = 0, with displacement = 0. For this answer, I would like to assume your reference point is releasing an object of mass M from h=max, in a pendulum model.
- Joe
A:

Hello Joe,

For small oscillations of a pendulum the usual harmonic motion solution is θ = θ0Sin(ωt) where θ0 is the maximum amplitude.   For large oscillations the motion is much more complicated.  Differentiating this once gives the velocity  =  dθ/dt = ωθ0Cos(ωt)   which, as you point out, is zero at the maximum excursion.   The acceleration, 
d2θ/dt2 = - θ0ω2 Sin(ωt),  on the other hand, is greatest at the the maximum excursion. 

You can see all the gory details at .

 

Leeh

 

 

 

 


(published on 07/08/2014)

Follow-up on this answer.