Hi all, I have one from a sample exam paper I don't know how to approach. I feel stupid for not knowing but I have tried a few things but am getting nowhere. Here it is: "The mass (m) hanging on an elastic band moves according to the equation [m*(d2s/dt2) = - mg/p(s-L)],
where (s) is the displacement of the mass, (L) is the natural length of the band and (p) is the constant parameter (called reference elongation). Find s as a function of time subject to the initial conditions:

s = s(subnaught), ds/dt = 0 when t = 0.

Any help would be vastly appreciated.

Regards, Rick

Question

Hi all, I have one from a sample exam paper I don't know how to approach. I feel stupid for not knowing but I have tried a few things but am getting nowhere. Here it is: "The mass (m) hanging on an elastic band moves according to the equation [m*(d2s/dt2) = - mg/p(s-L)],
where (s) is the displacement of the mass, (L) is the natural length of the band and (p) is the constant parameter (called reference elongation). Find s as a function of time subject to the initial conditions:

s = s(subnaught), ds/dt = 0 when t = 0.

Any help would be vastly appreciated.

Regards, Rick

anonymous · Answer

Cancel the m's and integrate twice.  Your initial conditions will tell you what to substitute in for your constants of integration (capital C's in the antiderivatives).

More detail upon request; hope this helps!