VibrationsΒΆ

Consider an example of the motion of a certain spring-mass system that is modeled by the following differential equation subject to the initial conditions:

\[ \frac{{\text d}^2 y}{{\text d}t^2} + \frac{{\text d}y}{{\text d}t}+ 1.25\,y = 3\,\cos t , \qquad y(0) =2, \quad y'(0) = 3. \]
Its solution can be broken into sum of the transient yc and steady state solution U(t)

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