# Manipulating equation

by romd
Tags: equation, manipulating
 P: 7 Hi, I need help manipulating the equation x(t)=e^(-t/tau) sin(omega*t) into a straight line graph (y=mx+c) of position (x) against time (t) Thanks in advance! edit: this might have been better off in the homework/coursework section, sorry
 PF Patron P: 3,923 Do you mean x = m.t + c ? Are you allowed to make co-ordinate transformations ? The equation describes a damped oscillator so there doesn't seem to be any other way.
 P: 7 Thanks for the reply! Probably, I just know I need a straight line out of it.. I think its a little beyond my knowledge, given my college teacher has no idea either. Once I have the equation I'll be set.
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## 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.

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