automatic substitution within functions?

The w in sin(t*w) does not refer to whatever the object with identifier w in the current scope. There isn't a way to get Python to work like this. You need to do something like:

sage: var('t, w')
(t, w)
sage: params = {w: 2}
sage: f(a,b,c,d,e,f,g,t) = sin(t*w)
sage: f.subs(params)
(a, b, c, d, e, f, g, t) |--> sin(2*t)

You just have to define the replacements you want once in a dictionary. You still have to call subs once for every function you want to change.

I think I'm just explaining Mike's answer a little, but I think that you should be able to define a dictionary

sage: params = {m1:1,m2:0.5,l1:1,l2:0.5,g:9.8}

and then do f.subs(params) as above. In his example,

var('t, w')
params = {w: 2,d:1,c:1}
f(a,b,c,d,e,f,g,t) = sin(t*w*d-c)
g=f.subs(params)
g

should do it. Mike, is that extra thing necessary, given that the arguments are the same in both cases?