Really stuck with this question:

The suspension in a car acts like a

damped harmonic oscillator, that is, the oscillations in

the suspension rapidly die down with time. A model for this includes both exponential

and trigonometric functions. Suppose the displacement in a car's suspension is given by

s(t)=e^{-t/2}cos(2t)

(i) Sketch the displacement of the suspension for 0 >=t>=2

and describe its behaviour (>= meaning greater than or equal to)

in a few words.

(ii) Show by direct substitution that the displacement satisfes the differential equation

4^{d^2s/dt^2}+4^{ds/dt}+17s=0

I am so lost on what to do, some suggestions whould be wonderful!

Nettie.L