Re: Partial differential equation problem

Sorry. I went mad for half an hour. Please ignore this.


"Robert Lully" <robert.lully@xxxxxxxxxxx> wrote in message
news:YoadnXstx5Df5mDYRVnysQA@xxxxxxxxxxxxxxx
Two weights are connected by a spring to each other, and each weight also
connected by a spring to a fixed wall. The masses of the weights are the
same, and so is the spring constant (k) for all 3 springs. Each spring is
3
units long. At t = 0, m_1 is at x_1 = 2, but m_2 is at its equilibrium
position of x_2 = 6.

I think the differential equations ought to be:

m d^2 x_1 / dt^2 = -k x_1 - k (x_1 - x_2)

m d^2 x_2 / dt^2 = -k x_2 - k (x_2 - x_1)

I divide through by m, and let k/m = 1.

The first integration gives:

d x_1 / dt = - x_1 ^2 + x_2 x_1 + c_1 = 0

d x_2 / dt = -x_2 ^2 + x_1 x_2 + q_1 = 0

Substituting the starting values for x_1 and x_2 gives -8 and 24 for c_1
and
q_1.

The next integration gives:

-1/3 x_1 ^3 + 1/2 x_2 x_1 ^2 - 9 x_1 + c_2 = 0

-1/3 x_2 ^3 + 1/2 x_1 x_2 ^2 + 23 x_2 + q_2 = 0

Is all this right? If it is, how can I calculate c_2 and q_2?

Thanks for any help.

Robert







.