In a pendulum without the small angles approximation the equation describing the motion of the mass is: $$\ddot{\phi}(t)=-\dfrac{g}{l}\sin\left(\phi(t)\right)$$ Applying a sinusoidal force $F(t)=A\sin(\omega t)$ to the mass $m$, the equation of the pendulum becomes: $$\ddot{\phi}(t)=-\dfrac{g}{l}\sin\left(\phi(t)\right)-A\sin(\omega t)$$ Is there any analytical method to solve this equation in order to find the possible resonances? Thanks
2026-03-28 10:03:57.1774692237
Forced oscillation in a pendulum and resonances
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