I have some difficulties regarding oscillation and SHM, i hope someone makes it clearer to me. Firstly, I don't have a good intuition of the formulas for velocity and acceleration as functions of time. I have no idea why the negative sign is present in the formula and what it's supposed to mean & adjust. I tried to derive at on my own but there was no negative sign Secondly, the period of a string doesn't depend on the amplitude, right ? In case I have a vertical string with some mass attached to it, isn't this mass supposed to change the equilibrium position of the spring, and then I don't account for it in my calculations as i use the new equilibrium position ? How can being in an accelerating elevator affect the period however the formula for the period seems not to relate ??