Equations for an Oscillating Pendulum

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

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)