Simple Harmonic Motion equations (part 2)?

Question

that last question: directions: determine an equation describing the motion of tides, assuming high tide at t=0.
5) reffering to q.4) how far does the tide in the bay drop 1 hour after high tide?
6)The brightness of the star Delta Caphei varies sinusoidally between values of 4.35 and 3.65. The time between maximum brightness readings is 5.4 days. Determine an equation describing the star's brightness as a function of time, assuming that its brightness at day 0 is 4 and decreasing.

Answer 1

The equation of simple harmonic motion is:

x(t) = A sin(wt + p) + C

where:

A is the amplitude (mean to peak) of the oscillation
w is the angular rate of change
p is the phase
C is a constant offset

In many situations, w is represented as (2 x pi x f) where f is the frequency.

Sin is a function that oscillates between +1 and -1. If the observed oscillation is between X and Y, then

X = C - A
Y = C + A

If the period of oscillation is T, then the frequency f is 1/T

That only leaves the phase. If you know x(0), then you know sin(p). That plus knowing whether the value is rising or falling at t = 0, lets you compute the proper value of p.

Just make sure that when you do the calculations, you use consistent units.