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Manipulating equation 
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#1
Feb108, 10:32 AM

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 


#2
Feb108, 10:54 AM

PF Gold
P: 4,087

Do you mean x = m.t + c ?
Are you allowed to make coordinate transformations ? The equation describes a damped oscillator so there doesn't seem to be any other way. 


#3
Feb108, 10:58 AM

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. 


#4
Feb108, 11:16 AM

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Thanks
PF Gold
P: 39,682

Manipulating equation
The question is "make a straight line out of what"? The graph of the function you give, [tex]x(t)=e^{t/\tau} sin(\omega t)[/tex], in the "txplane" 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: [itex]y= me^{t/\tau} sin(\omega t)+ b[/itex]. 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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