Simple pendulum subject to a driven force

LCSphysicist · Jul 9, 2020

Printed textbook problem 4-5 on a simple pendulum of length 1 m with its support driven horizontally, showing the equation d²x/dt² + γ dx/dt + (g/l)x = (g/l)ξ and the instruction to solve for steady-state motion with ξ = ξ₀ cos ωt.

The problem is how to construct the right diagram of forces actually

Hand-drawn free-body diagram of a simple pendulum: a ball hangs from a pivot on a horizontal bar, with red arrows labelled w (weight), -bv (damping), +Fo cos wT (driving force) and -Fo cos wT (driving force at the pivot), and a black velocity arrow labelled v.

Unfortunately, the Fo*cos acting on the ball will not carry the g/l of the solution

-mg*sin(´p) + (-bv) + (Fo*cos(wt)*cos(p)) = mx''
Fo*cos(wt) = mx'' + mg*x/l + bv

haruspex · Jul 9, 2020

LCSphysicist said:

Homework Statement:: All below
Relevant Equations:: All below

View attachment 266128
The problem is how to construct the right diagram of forces actually

View attachment 266129

Unfortunately, the Fo*cos acting on the ball will not carry the g/l of the solution

-mg*sin(´p) + (-bv) + (Fo*cos(wt)*cos(p)) = mx''
Fo*cos(wt) = mx'' + mg*x/l + bv

You do not care what force is applied at the point of suspension. You only care where that point is at time t, and how that affects the angle of the pendulum.

Simple pendulum subject to a driven force

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