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deedsy
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Homework Statement
A simple pendulum consists of a point mass m suspended from a fixed point by a weightless rigid rod of lengh l.
The kinetic energy = 1/2*m*l^2*(dθ/dt)^2
The potential energy = -m*g*l*cosθ
Calculate the time averages of the kinetic and potential energies over one cycle, AND compare them with the total energy of the system.
Homework Equations
(d^2θ/dt^2) + (g/l)sinθ = 0 ∴ w = √(g/l)
τ = 2∏/ω
The Attempt at a Solution
T = 1/2ml^2 (ω)^2
T = 1/2mlg
U = -mglcos(wt)
U = -mglcos(√(g/l) * (2∏√l/g))
U = -mglcos(2∏)
U = -mgl
So 2T + U = 0
Is this the correct answer? Because I thought T should = U?