# Spring DE

Can someone help me set up the DE needed for the following problem, there are other similar ones in my booklet so any help with this one should be helpful for the other questions.

Q. A mass of 100kg is attached to a spring suspended from the ceiling of a room, causing the spring to stretch 20 cm upon coming to rest at equilibrium. The spring is then pulled down 5 cm below the equilibrium point and released. Assuming there is no damping and that no external forces are present, determine the equation of motion of the mass and express the downward extension of the spring, x m, from the equilibrium position as a function of time sec., which has elapsed since the mass was released. Also determine the amplitude and period of the motion.

I really only need help with setting up the equation of motion. I haven't seen problems of this type before so I'd like some help. Any pointers would also be good, thanks.

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LeonhardEuler
Gold Member
Well, here's how to start. $\vec{F}=m\vec{a}$ This is basically a 1-dimentional problem so rather than a position vector, a single variable x will denote the displacement from equilibrium. Then this equation becomes $F = m\ddot {x}$ Now you need to make a substitution for F in terms of x and you will have a differential equation. The substition will be the forces acting on the body. What forces are these?

Thanks for the help. I'll need to think about the wording of the question a bit more before I can determine an expression for F.

PS: I'm a very weak physics student so it'll probably take me a while. Last edited: