Why is the accel. zero as a spring passes through the equilibrium pt. on its way up after being pulled down?

Question

Background info: A spring oscillates with a weight on it in simple harmonic motion.
This is another physics lab question.... please help!

here is the full question: Explain, in terms of force, why the acceleration is zero as a spring passes through the equilibrium point on its way up after being pulled down.

Answer 1

When the spring is at its equilibrium position without pulling on it the net force on the spring is 0. Think of a way to get the force on the spring equal to 0 using the equation F =kx. It is F = k 0 where the x position is 0, the spring constant will not change so you will have to call that x position 0. That x position where the net force is 0 is a crucial piece of information. Another way to see the implications of a 0 force is to use F =ma which is F = ma = kx = 0 . Therefore F = m 0 = 0 because mass wont go to 0 it is the acceleration that is 0.

When you pull on the weight you give the system potential energy which is dependent on the x position. It is P = 1/2 kx^2 . So when the x is at the 0 position your potential energy is 0, but of course you know that it will travel pass that x position because you cant get rid of the energy. It has all been converted to kinetic energy. When its moving past the x =0 position it can be hard to imagine that the acceleration is 0 because its moving. But you have to keep in mind that a 0 acceleration does not mean that it wont move. All it means is that you do not have any outside forces on the system. The reason for the movement of the weight is not dependent on outside forces but, that initial force you gave it in order to give it potential energy.