Classical Dynamics Question?

Question

"Consider a mass m hanging vertically from the end of a spring of force constant k. In equilibrium, the mass rests at a position y = y0 = mg/k. Starting from Newton’s second law, show that if the mass is displaced from equilibrium a distance A and then released, it will follow simple harmonic motion about the position y0." Good luck!

Answer 1

Just write the differential equation and solve it, and you'll see that it follows simple harmonic motion.