# Simple harmonic motion on a vertical spring

Say we have a spring attached vertically to a wall. Now, let's assume that we attach a mass to the spring, but we do not let the spring extend just yet (we could hold the mass on our palm for example). Now, based on my understanding, a new equilibrium position should be established below our current equilibrium position (perhaps it hasn't been established yet, that might be the source of my misunderstanding). So technically speaking, right now, relative to the new equilibrium position, the spring is compressed. That seems very counterintuitive to me because it would seem odd that suddenly, just by attaching the mass and without having the spring move at all, there is compression of the string (i.e a force). Also, say we now release the mass (suddenly, not slowly). It appears to me that it will come back to this initial position it was at, and if that's really what happens, I would say it's intuitive that the spring is compressed. It's just the first step that's giving me trouble. Could someone please point out my source of misunderstanding?

The spring is compressed relative to the new equilibrium, but that is not the same thing as saying the spring becomes compressed relative to it's unstretched/uncompressed position. If you are holding the mass at the unstretched/uncompressed length of the spring then the spring won't exert a force on the mass when you attach it.

• Right so here's my followup question: the moment we let go of the mass, the spring will stretch (relative to the initial equilibrium position) so now the spring will exert an upward force, no? So the mass will not yet be in its final state of SHM correct? Because at its current position, relative to the new equilibrium position, we would expect the spring to be exerting a downward force right? (since it's compressed relative to the new equilibrium) Jul 13, 2019 at 16:40
• @user10796158 Compressed relative to the new equilibrium doesn't mean the force is downwards. With the mass on the spring it is not the case that the spring force changes sign around equilibrium. The net force is what changes sign around equilibrium. As soon as you release the mass SHM will start. Jul 13, 2019 at 17:21
• ahh I was confusing net force and spring force makes sense now thank you. Jul 13, 2019 at 17:43

About the compressions. ..when considering SHM on a vertical spring...the compression and streching of the spring is always with respect to the equillibrium position or also known as mean position....

The equilibrium position is where the net force of the system is zero now by system its only the spring and mass....any other additional force you provide (lets say holding the mass up) is external and not belonging to the system so it compress or stretch the spring. (In your case you provide an additional force upwards which dosnt belong to the system hence compressing the spring).....so you should remove such forces before locating the equilibrium position..and the compression or streching (rarefaction) of the spring should be calculated from this equilibrium position...

Note that you might consider the system to be in equilibrium when you hold the mass up....but this is not the equilibrium position....its just equilibrium. ...the equillibrium position is when the spring balances the weight on its own....so as soon as the weight is released it tends to move down and comes to the equilibrium position....

Another fact is that...with respect to the equilibrium point before adding the weight...the spring is now streched ... and with respect to the now equilibrium point. ..the spring was previously compressed.....its all with respect to each other but in SHM we mostly consider the new equilibrium points as the reference and ignore the previous once

So your spring is clearly compressed when you hold the weight up with your palm even though the spring didnt move . And when you release the spring it wont come back to the initial position but travel harmonic motion (cant be sure its a SHM) and come back to the newly formed equilibrium position... (assuming its a small weight cause if the weight is large then the spring stretches excessively and may not come back up to the equilibrium position)