First, the equation:
Now, the explanation, term by term.
"30" represents the "natural" height of the center of the axle above the ground.
"20" represents the initial amplitude of the bump.
" " means that every half second, the amplitude of the bump decreases by 80%
" " is used because when t=0, the truck has just hit the bump and is 20cm above its natural height, beginning its decline, hence the entire term =+20 at t=0.
" " is used because the period of the bounce is half a second and the argument should be for period P.
"3" represents the amplitude of the point spinning around the axle. (half the diameter)
"sin" is used arbitrarily, as the problem does not state the orientation of this point at the exact moment the truck hits the bump.
" " is the argument used because the axle has a period of 1 second.
Graph these three terms separately and it is easy to see. The straight line at h=30 represents the trucks "natural" height above the ground, the equilibrium of the system. The cosine term is a half second period bounce steadily decreasing in amplitude, and the sine term represents the point on the axle happily spinning round.
Lastly, we appeal to the Law of Superposition, which despite it's scary name, simply means that by adding all the separate terms governing this motion together, we get the end result of this motion, albeit a complicated-looking graph.