Hello, I have a question on how to do something. I'm not sure whether calculus or trigonometry is needed. this is not a homework question. an object will move left and right of a center point in a sinusoidal motion. the period is always the same; the amplitude should change. at any point in time F=kd, where F is the force pushing the object toward the center point, d is its distance from the center, and k is some constant. If i have the object's position and velocity relative to center and I push or pull it with a certain force (in addition to F), let's say "G", I need to predict where it will end up after one-half a period. I also need to factor in resistance -- the object will have some amount of resistance to its motion. The end goal is to do this many times with varying G's and calculate the amplitude at which it's moving back and forth at any particular time. so if position and/or velocity can be forgone completely so that we only arrive at intensity from G inputs that would work too. come to think of it, if the period is always the same then the thing can't adjust to a change in phase of an input frequency (i'm simulating sympathetic resonance here), so i'm not sure how sympathetic resonance adjusts to changing phase. that has to be accounted for too. also I need to know the ideal resistance for a given frequency so that the amplitude doesn't add up indefinitely.