# Math

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An external sinusoidal force is applied to an oscillating system which can be modelled by a model spring and a damper. The general solution of the equation of the motion is given by,

x = 5 + 3.071cos(2πt – β) + 3.14exp(-7.96t) cos(αt + φ)

where α, β, and φ are some constants.

Determine the amplitude of the oscillation when steady-state is reached. Give your answer correct to 3 decimal places.

• Math -

Since the steady state is just
x = 5 + 3.071cos(2πt – β)
then the amplitude will be 3.071

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