the word problem is:
A mass is supported by a spring so that it is at rest 0.5 m above a tabletop. The mass is pulled down 0.4 m and released at time t = 0, creating a periodic up and down motion that can be modelled using a trigonometric function. It takes 1.2 seconds to return to the lowest position each time.
so i know it will be a sin(x) graph, and i know it starts 0.5m above ground level, therefore the vertical shift is 0.5m - that will give us:y = a sin (x) + 0.5the mass will be pulled down 0.4, and will rise 0.4 above where it was stationary (so 0.4m + 0.5m = 0.9m is the maximum). I can determine the amplitude: (0.9 - 0.8)/2 = 0.4, so that will give us:
y = 0.4 sin (x) + 0.5the only two things i'm not sure about is the phase shift and the horizontal stretch.
9/10? so the equation would be:
y = 0.4 sin (5/3pi [x-9/10]) + 0.5
i'm not sure if it's -9/10 or +9/10
but the standard form for the equation is y = a trig [ n ( x - h) ] + k
so since it's 9/10 (positive, not negative), and pos * neg = neg, i'm guessing it's:
y = 0.4 sin (5/3pi [x-9/10]) + 0.5
right?
EDIT: I just graphed it and found out it's +10 because it's moving right. thanks for your help!!