In Simple Harmonic Motion questions involving tides when forming an equation like x=a - b cos(nt), how do i tell when to use + or - ?
Thank you
It depends on which where you want x to start (at t = 0).
Note that cos(t) starts at its maximum (and begins moving to the minimum extreme) whilst -cos(t) starts at its minimum (and begins moving towards the maximum extreme).
So if you wanted a Simple Harmonic Oscillator to start at its maximum extreme, you'd have x(t) involving a +cos(t). If you wanted it to start at its mnimum extreme, you'd have x(t) involving a -cos(t). (In both these cases, the initial velocity is 0. It helps to visualise a pendulum or spring for these SHM questions.)
