Solve system of 2nd order ODE?

Questions
1

New to Mathematica. Need to plot the position and velocity of 14 points. 2 are fixed 12 are in the form of a system of equations. what mistake am I making?

g = 10;
ic1 = {y[x, 0] == 0}

bc = {y[-1/2, t] == 0, y[1/2, t] == 0}

system = Table[
  D[y[x, t], {t, 
     2}] == -100 (2*(y[x, t]) - y[x - 1/13, t] - y[x + 1/13, t]) - 
    10 ((2*D[y[x, t], {t, 1}]) - D[y[x - 1/13, t], {t, 1}] - 
       D[y[x + 1/13, t], {t, 1}]) + g, {x, -1/2 + 1/13, 1/2 - 1/13, 
   1/13}]

functions = Table[y[x, t], {x, -1/2, 1/2, 1/13}]

DSolve[{system, bc, ic1}, functions, t]

Capture.PNG
Capture.PNG1436Ă—835 165 KB

2

You cannot give initial conditions as y[x, 0] == 0 with symbolic x. You must give the list of the initial conditions for all the specific values of x.

3

That didn’t work

4

This is very similar to what you provided.

g = 10;
system = Table[D[y[x, t], {t, 2}] == -100 (2*y[x, t] - y[x - 1/13, t] - y[x+1/13, t]) -
    10 (2*D[y[x, t], {t, 1}] - D[y[x - 1/13, t], {t, 1}] - D[y[x+1/13, t], {t, 1}]) + g,
    {x, -1/2 + 1/13, 1/2 - 1/13, 1/13}];
functions = Table[y[x, t], {x, -1/2 + 1/13, 1/2 - 1/13, 1/13}];
DSolve[system, functions, t]

It doesn’t incorporate any initial or boundary conditions and thus should only return the general solution and it appears to be very slow because of the number of equations involved, but it doesn’t appear to give any warning or error messages.

Perhaps if it finishes you might be able to then apply your conditions and obtain the specific solution that you are looking for. Or you might try adding conditions one at a time and try to interpret the warning and error messages to see if you can make those additions acceptable.

5

I would try NDSolve first, adding initial data as needed. If that works, there may be some hope for a symbolic solution.