How does one sketch the derivation of the equation of motion for a planar pendulum of length l and mass m in constant gravity g, subject to a constant torque force F (directed along the tangent to the circular trajectory of m). I know that the normal derivation for an undamped and unforced pendulum would be: $$\theta''+ksin\theta=0$$ I am unsure however on how to add the constant force aspect?
2026-03-29 22:12:24.1774822344
Constant Force Pendulum (undamped)
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The net force on an object is equal to mass times acceleration, hence $$\vec F+k\vec x=m\vec x''$$ where $x$ is the (linear) distance from the equilibrium position. The vectoral sum of the applied force $\vec F$ and the restoring force $kx$ may not be in a particularly understandable direction, but the equation holds.