question about spring restoring force

[scrub2scrubs]

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So I was doing a problem about springs that wanted you to calculate the final velocity that the spring had at the equilibrium point after it had been compressed. I know that solving this problem in terms of energy is probably the easiest way to go about it, but I tried something else.

I first used hooke's law to calculate the force and then calculated the acceleration from there. Afterwards I used kinematics to solve for the velocity, but I kept getting a different answer.

I think I know why but I'm not sure. Is the reason you can't use kinematics because the restoring force is always changing depending on where the spring is? So, since the force is constantly changing, the acceleration is constantly changing, so therefore kinematic equations can't be used?

 

[dudewheresmymd]

Yes F=-kx & F=ma, as "x",the displacement from equilibrium changes, the f changes and therefore the acceleration is changing and is NOT constant (another way to recognize that acceleration is not constant is because the acceleration of a pendulum or box system is greatest at maximum displacement from equilibrium and = 0 at equilibrium) . Therefore, you cannot use the kinematics equation as they only apply for constant acceleration.