Ok, thanks so far. Let me try to understand what's happening here.

a numeric solution of the ode,

specifically telling the programm that c[r], m[r], c[g], k[g], k[r], m[g] are parameters,

assigning values to those parameters,

values of x[g], x[r] and their diffs in relation to t.

Is there a way of getting the solution without assigning values to the parameters?

Hm, if I set t to a high value, like 250, the results for the x's get way to high, for they should actually tend towards 0

may this be a problem of the calculation or rather an error in my initial ode or ics?

Ok, thanks so far. Let me try to understand what's happening here.

a numeric solution of the ode,

specifically telling the programm that c[r], m[r], c[g], k[g], k[r], m[g] are parameters,

assigning values to those parameters,

values of x[g], x[r] and their diffs in relation to t.

Is there a way of getting the solution without assigning values to the parameters?

Hm, if I set t to a high value, like 250, the results for the x's get way to high, for they should actually tend towards 0

may this be a problem of the calculation or rather an error in my initial ode or ics?

Sorry about that, didn't notice they were images.

ode := m[r]*(diff(x[r](t), `$`(t, 2)))+c[r]*(diff(x[r](t), t)-(diff(x[g](t), t)))+k[r]*(x[r](t)-x[g](t)) = 0, m[g]*(diff(x[g](t), `$`(t, 2)))+c[g]*(diff(x[g](t), t))+c[r]*(diff(x[r](t), t)-(diff(x[g](t), t)))+k[g]*x[g](t)+k[r]*(x[r](t)-x[g](t)) = 0

ics := x[g](0) = 0, (D(x[g]))(0) = 1, x[r](0) = 0, (D(x[r]))(0) = 1

dsolve([ode, ics], {x[g](t), x[r](t)})