The most general answer looks like A cos ωt - φ. And what’s the solution to this equation? I think we did a lot of talking and said look, we are looking for a function which, when differentiated twice, looks like the same function up to some constants, and we know they are trigonometry functions.

But if you pull it so the mass comes here, you move it from x = 0 to a new location x then, there is a restoring force F, which is - kx, and that force will be equal to mass times acceleration by Newton’s law, and so you’re trying to solve the equation d 2x/dt 2 = -k/m times x, and we use the symbol, ω 2 = k/m, or ω square root of k/ m. This spring has a certain natural length, which I’m showing you here.

The standard textbook example is this mass on spring. Professor Ramamurti Shankar: Stable equilibrium, and if you disturb them, they rock back and forth and there are two simple examples. Example Equations of Oscillating Objects Fundamentals of Physics I PHYS 200 - Lecture 17 - Simple Harmonic MotionĬhapter 1.