Forced vibration

Forced vibration with dampening

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Consider the differential equation

y'' + 0.125 y' + y = 3 cos(ω t), y(0) = 2, y'(0) = 0, where ω = [omega].

The solution is

y = [some number]e-t/16 cos(sqrt(255) t / 16 - [delta] ) + [some number] cos([omega] t - [delta]).

Move the slider to change the value of ω. The current value is ω = 2.

Forced vibration without dampening

Consider the differential equation

y'' + y = cos(ω t), y(0) = 0, y'(0) = 0, where ω = [omega].

The solution is

y = ((2/(1 - omega^2)) sin((((1- omega)t)/2)) sin(((1 + omega)t)/2)

Move the slider to change the value of ω. The current value is ω = 2.

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