# Energy in simple harmonic motion ─ where is the kinetic energy stored, and where is the potential energy?

When a mass connected to a spring is in simple harmonic motion and somewhere between the mean and extreme positions the mass is cut from spring. Then instantaneously after cutting the mass will only have its kinetic energy right? (Or it will have total energy kinetic+potential?)

Or I mean to say that in a system in simple harmonic motion, the kinetic energy is stored in the mass while the potential energy is always stored in spring. Am I correct?

• It could have a potential energy as long as it's on a particular height above ground... – Nehal Samee Feb 14 '18 at 11:41
• I am talking about elastic potential energy – Ava Feb 14 '18 at 11:42
• Elastic potential energy is stored in the spring ...Cause its extension causes the potential energy to be stored... – Nehal Samee Feb 14 '18 at 11:44
• You are right because generally we talk about massless springs and obviously they can't store kinetic energy = $\frac12 mv^2$. – Archer Feb 14 '18 at 11:45
• But we usually say that the energy of Bob/mass in SHM is constant that means we say that it has PE. – Ava Feb 14 '18 at 11:46

You are quite correct. Elastic potential energy is always stored in the spring. Then why does the block move when compressed though it does not have any energy?

Let us consider a situation in which a spring is compressed by a (non attached) block. When compressed the spring will acquire elastic potential energy given by

$$U_i=\frac {1}{2}kx^2$$

Any system acquiring any energy will always configure to a position such that it has minimal energy. So the spring will move towards its equilibrium position. In this process the block also moves as it is in immediate contact with the spring. Thus gaining kinetic energy.

The block reaches maximum speed when the spring reaches its equilibrium length - that's the point where all the energy stored in the spring is converted to kinetic energy. And the law of conservation of energy is also consequently followed.

• I didn't ask why does a block move when it has zero energy... – Ava Feb 22 '18 at 11:39
• Yeah...But it also answers your question.. – Jnan Feb 22 '18 at 12:34
• No it doesn't I want to confirm that if I cut the spring at position where the block has both KE and PE, what will be the energy of block just after – Ava Feb 22 '18 at 17:04
• It will have its kinetic energy. – Jnan Feb 22 '18 at 17:33
• There is Only KE no PE? – Ava Feb 22 '18 at 17:49

While the mass is not cut from the spring, there is transfer of energy. This is the transfer of potential energy into kinetic energy of the mass.

When you cut the spring, the block will proceed to move with the kinetic energy it had before. The potential energy in the spring will not disappear or somehow suddenly transfer to the mass but it will remain in the spring. Ideally the spring will keep oscillating which maintains that same energy. In practice the energy will slowly dissipate until it stops oscillating due to friction and other forces. When the spring is cut the potential energy doesn't go anywhere, it remains in the spring system (from which the mass escaped). There is no way for energy to transfer from the spring to the mass because the mass is no longer in contact.