A bouncy ride

A truck of mass $m = 1000$ kg without shock absorbers (so that there is no damping) rests on suspension springs of a combined effective spring constant $k_{\mathrm{eff}}$ such that the full weight of the truck compresses the springs by 2.5 cm. Before $t=0$ the truck is riding smoothly along (the springs are in their equilibrium position), but at $t=0$ the truck hits a bump which gives it an initial upward velocity of 10 cm/s from the equilibrium position. You may take the equilibrium position to correspond to $x=0$.

(a)

Find the effective spring constant $k_{\mathrm{eff}}$.

(b)

Write down the equation of motion of the object.

(c)

Using the complex representation, find the particular solution $x(t)$ to the object's equation of motion for $t \ge 0$.

(d)

What is the amplitude of the resulting oscillations?