Manipulating equation

by romd
Tags: equation, manipulating
romd is offline
Feb1-08, 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
Phys.Org News Partner Science news on
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
Mentz114 is offline
Feb1-08, 10:54 AM
PF Gold
P: 4,081
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.
romd is offline
Feb1-08, 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.

HallsofIvy is offline
Feb1-08, 11:16 AM
Sci Advisor
PF Gold
P: 38,894

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 "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:
[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.

Register to reply

Related Discussions
[SOLVED] Manipulating a formula Introductory Physics Homework 15
Manipulating sin/cos functions Calculus & Beyond Homework 13
Kinematic Equations - Manipulating them. Introductory Physics Homework 1
manipulating the TISE for a SHM Advanced Physics Homework 8
Manipulating your brain Biology 0