Order the derivation of simple harmonic motion from Hooke's law.

1. Write Hooke's law: the restoring force is F = -kx
2. Substitute into Newton's second law to get m times the second derivative of x equal to -kx
3. Divide by m to reach the second derivative of x equal to -(k/m) x
4. Recognise the standard form with omega squared equal to k over m
5. Conclude the solution is the sinusoid x(t) = A cos(omega t + phi)

This is the whole lesson in five lines: a linear restoring force plus the second law gives a second-order differential equation whose solutions are sinusoids. The minus sign is essential, it is what makes the force restoring, and without it the solutions would grow exponentially instead of oscillating.