# Simple Harmonic Oscillation of a vertical Spring

If a spring with a spring constant of k is hung vertically, and a mass is attached to it the spring will rest in equilibrium at some distance h from the springs original equilibrium length because the spring force must equal the gravitational force. Now lets say I pull the mass down some distance, and I let go, obviously, it will begin to oscillate. But, I am confused whether the center of oscillation will be at distance h, or about the spring's original equilibrium length.

• -1 Why don't you get hold of a spring or elastic band and try it? – sammy gerbil Jan 15 '18 at 17:51

## 1 Answer

It will be about the lower point.

Imagine the spring is 10 meters long hanging from a tree branch 16 meters off the ground (so the end of the spring is 6 meters up). You climb up a ladder and add a large mass to the spring, stretching it by 5 meters, to 15 meters in total length. It's resting there quietly, one meter off the ground. Then you pull the mass down 1 centimeter, and let it go. What happens? Does it jump back up to 6 meters in the air?