A Damped Sinusoidal Function

math simulation

Instructions: Change the slider to change the damping envelope.
Explanation: An oscillator's amplitude will decrease over time. How quickly depends on the damping. The basic cosine function is shown in dark blue. $$ y = \cos(\omega t)$$ If this is multiplied by a decaying exponential $$\textrm{damping} = e^{\frac{-bt}{2m}}$$ then the amplitude of oscillation will decrease over time. $$y_\textrm{damped} =e^{\frac{-bt}{2m}} \times \cos(\omega t)$$ This sim allows the user to change the damping term and see how that changes the oscillations over time.

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Tags:

decaying sin function
time constant

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