1. A mass M is attached to a spring of stiffness $\omega^2 M$ and is set in motion at $t = 0$ by an impulse force $P$. The equation of motion is $$Mx'' + M\omega^2 x = P \cdot \delta(t).$$ Obtain an expression for $x$ in terms of $t$.
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$$M s^2 X(s) + M\omega^2 X(s) = P$$ $$X(s) (M s^2 + M\omega^2) = P$$ $$X(s) = \frac{P}{M(s^2 + \omega^2)}$$ Show more…
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