How to solve simple harmonic motion problems using initial conditions

We have seen how the general solution for simple harmonic motion involves sines or cosines. These functions are periodic functions, and it makes sense that they are used to solve period motion problems. But what about problems where we are given initial conditions (i.e. at t = 0)? How do we find specific solutions to specific problems? Well, here is an example of how to do this. We will have a case where a mass oscillating on a spring has BOTH initial position and initial velocity. We introduce the general solution that involves a phase angle. Check it out.