# Manipulating equation

by romd
Tags: equation, manipulating
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,569 Manipulating equation The question is "make a straight line out of what"? The graph of the function you give, $$x(t)=e^{-t/\tau} sin(\omega t)$$, in the "tx-plane" is certainly not a straight line and there is no y. The graph of that would be a "wave" getting smaller and smaller as t increases. Sometimes you can make a function into a linear graph by plotting the logarithms of the values rather than the values themselves, but that won't work with that "sin" there. Perhaps you mean that, given this x value, as a function of t, find the corresponding y value on the line y= mx+ b. That's easy- just substitute that function for x: $y= me^{-t/\tau} sin(\omega t)+ b$. The values given by those functions will give the position, at time t, of an object moving along the line y= mx+ b.