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# Just solving 2 simultaneous differential equations - am i being thick!? watch

1. Ok, am I just being stupid?

Aim is to find x(t). alpha, g, M and m are all constants.

I've tried just solving it as a standard second order ODE but can't really get much further than the complementary function.
Attached Images
2. Problem.pdf (79.1 KB, 95 views)
3. I'm not convinced of some of your manipulation; it seems you've written .

But aside from that, find the complementary function, the extra term on the RHS is just a constant, so look for a PI of the form x = K for some constant K.
4. Sorry, i meant sin(2alpha)/2. Will have a go now..
5. (Original post by 3thr3e)
Sorry, i meant sin(2alpha)/2. Will have a go now..
Yes. After the correction integrate the equation twice with respect to x.
6. (Original post by DFranklin)
I'm not convinced of some of your manipulation; it seems you've written .

But aside from that, find the complementary function, the extra term on the RHS is just a constant, so look for a PI of the form x = K for some constant K.
IGNORE. I'm BEING THICK as suspected!
Attached Images
7. Untitled.pdf (91.1 KB, 63 views)
8. (Original post by imzir)
Yes. After the correction integrate the equation twice with respect to x.
You can't just do that though can you. x is a function of t..
9. (Original post by 3thr3e)
You can't just do that though can you. x is a function of t..
sorry i meant integrate x with respect to t. sorry I am an alevel student.
10. (Original post by imzir)
sorry i meant integrate x with respect to t.
that's like saying what's the integral of y with respect to x and not knowing what the function y is!
11. (Original post by 3thr3e)
that's like saying what's the integral of y with respect to x and not knowing what the function y is!
ive done second order differential equations before but this looks wierd for some reason.

12. (Original post by DFranklin)
I'm not convinced of some of your manipulation; it seems you've written .

But aside from that, find the complementary function, the extra term on the RHS is just a constant, so look for a PI of the form x = K for some constant K.
Ok I think i've done it. Please could you check it?
Untitled2.pdf
13. The broad strokes are there, but you also need to consider the particular integral to make your solution complete.

I have appended the detailed workings below for your reference, hope it helps. Peace.

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