Resonance Calculator: Step-by-Step Solutions

Amplitude response curves and the resonance frequency. Every step of the solution is shown, as you would write it on paper, using exact fractions.

What it solves

For $m{x}^{\prime \prime }+c{x}^{\prime }+kx=F_0\cos \omega t$ the steady-state amplitude is $M(\omega )=F_0/\sqrt{(k-m{\omega }^2{)}^2+c^2{\omega }^2}$. See how it depends on the forcing frequency and on the damping.

How to use it

1. Enter your own numbers or functions in the boxes (an example is already filled in, or press Random example).
2. Check the equation preview, then press Solve step by step.
3. Reveal the solution one step at a time with Next step, or show everything at once.

Need the theory first? Read Section 5.5: Resonance, which explains the method in small steps with worked examples and exercises, then come back and test yourself with the Chapter 5 quiz.

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