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

waynex · Answer

You have a linear second order differential equation. Which of the usual techniques have you attempted to use to solve this? What is s=(subnaught)?