Consider the following problem
I pull a mass m resting at x = 0 on a frictionless table connected to a spring with some k by an amount A and let it go. What will be its speed at x=0?
I know how to solve it using the law of energy conservation but as a challenge I wanted to find the solution without it.
So from the 2nd Newton's law it's obvious that a = k*x/m. But I don't know how to integrate it in order to find velocity since a = f(x(t)).
How would I solve this without using the law of energy conservation?