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Using Calculus to Explain Resonance

Here is a derivation for the differential equation of resonance. In Physics resonance occurs when the driving frequency matches the natural frequency and the amplitude reaches a maximum. Why is that? In this video we answer this question by first looking at a free oscillation to find an expression for the natural frequency. We then look at the case of a forced oscillation in which we apply a periodic force and find an expression for the amplitude. This is a derivation which is suitable for first year physics undergraduates, physics enthusiats, students interested in Physics Olympiads, JEE Main and Advanced Preparation. I hope this is useful!