How to get equation for velocity of Pendulum

Thread starter ortegavs
Start date Jan 23, 2011
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Pendulum Velocity

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SUMMARY

The discussion focuses on deriving the equation for the velocity of a pendulum using the formula for period T = 2π√(L/g). The user attempted to combine centripetal acceleration (a = 1/2 V²/r) with gravitational acceleration (a = g(sinθ)) to arrive at the velocity equation v = √(2gL(sinθ)). However, there is uncertainty regarding the validity of this approach due to the differing nature of the accelerations involved. A suggestion is made to start with the equation of motion θ = θ₀*cos(2πt/T) for a more accurate derivation.

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Understanding of pendulum motion and its equations
Familiarity with centripetal and gravitational acceleration concepts
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Basic grasp of differential equations related to motion

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Jan 23, 2011

ortegavs

Homework Statement

Homework Equations

T=2pi(sq.root L/g)

The Attempt at a Solution

combined a=1/2 V^2/r with a=g(sinO) then solved for v.
got v=Sq.root 2gL(sinO). Don't know if this is right.

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Jan 23, 2011

Delphi51

Homework Helper

I doubt if that approach works - the one acceleration is vertical while the other is radial.

I suggest beginning with the equation of motion
θ = θo*cos(2πt/T)