However, in a rational sence, they are controlling the Economy so as to smooth out the Highs and Lows (the Amplitude of the Waves).
I respectfully disagree. Have you ever heard of pilot induced oscillations or Edward Deming? Trying to control a variable, especially without enough information, leads to larger oscillations in the variable.
I agree with your 'disagreement': The very act of intervening in the system may have unforseen results. For example, [IMHO] Greenspan brought on the 'Crash of 1987' by his continued raising of interest rates in an effort to supposedly 'control inflation'. The Market got spooked, sell programs kicked in, everyone jumped for the 'exits' at once, and there was a massive downdraft in the market.
Nonetheless, the Fed does it because it can. In saying this I ascribe no 'right' or 'wrong' to my original answer. This is merely the explanation I'm sure you would get if you were to ask anyone, or that I remember from my undergraduate year of Macro- & Micro-Economic Theory.