# Homework Help: Differential Equations/Newton's 2nd Law

1. Jun 6, 2013

### BigJon

1. The problem statement, all variables and given/known data
a heavy object of mass m is suspened in a room through a linear spring whose spring constant is k. Initially the object is suspported so that the spring is at its free length (neither strecthed/compressed) which is take to be x=0. At time zero the support is removed and theobject is allowed to oscillatee under the combined influence of both gravity and spring forces. Using newtons second law of motion obtain the differential equation that describes the position x of the mass m relative to the undistrubed endpoint of the spring as a funtion of time

2. Relevant equations

F=ma,F=-mg,F=-kx

3. The attempt at a solution

So what is did was F=ma, F=-mg, F=-kx

a=d^2s/dt^2, F=ma=-kx=-mg so,

-kx-mg=m(d^2s/dt^2) solved for d^2s/dt^2 and got d^2s/dt^2=-(kx/m)-g

I dont have any idea if that is correct or not

2. Jun 6, 2013

### Ray Vickson

It is an absolute sin (worthy of losing marks) to use the same letter F to stand for three different things in the same problem. Instead, use, eg., F_g for the force of gravity, F_s for the spring force and F for the total force, or use some other letters entirely. However, your final DE would be OK, provided that by d^2 s/dt^2 you really mean d^2 x/dt^2, and provided that you regard positive x as pointing up, in the direction opposite to the force of gravity. (Think about why you need to specify a direction convention for x.)