http://img207.imageshack.us/img207/1980/ode.png

Can someone explain how to solve this? Cheers.

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- Dec 4th 2009, 12:41 PMHarisMass on a spring problem
http://img207.imageshack.us/img207/1980/ode.png

Can someone explain how to solve this? Cheers. - Dec 4th 2009, 03:59 PMlvleph
You will need to solve the homogeneous problem

Then you will find a particular solution you can do this using the method of undetermined coefficients. Then you add the two solutions together. - Dec 5th 2009, 08:31 AMHaris
Can you explain how to find the C.F.? Apparently its x=cos(wt)+sin(wt) ? I don't know how they got that answer though.

- Dec 5th 2009, 09:02 AMlvleph
Okay, I will go through the particular solution first. I will let denote the particular solution. Since the nonhomogeneous part is a trigonometric function we will let the particular solution be of the form . Now we must determine the coefficients . To do this we will plug back into the original DEQ.

and so

.

Thus we have

and

.

Therefore, we have

and

,

so

.

Finally, we see that our particular solution is

.

Deleted mistake see following post. - Dec 5th 2009, 09:15 AMlvleph
Sorry I made a mistake. The homogeneous solution is wrong. The solution of the characteristic equation is not . The solution is .

Therefore, the homogeneous solution is of the form

.

Finally, the general solution should be

.

To determine the constants we must have initial conditions.