For example, notice that the graph is at equilibrium (equals 0) and is downward sloping at x = .4, and that the graph is again at equilibrium and downward sloping at x = 2.4. According to this, the period is:
P = 2.4 - .4 = 2
The coefficient of x is b, where:
b = 2pi/P = 2pi/2 = pi.
So the equation should be:
2sin[pi(x - h)]
Where h is the shift in the graph. Recall that the normal unshifted sine function starts at equilibrium with an upward slope at x = 0. In this graph, we see that the function is at equilbrium with an upward slope at x = 1.4. Therefore h = 1.4. So the equation becomes:
2sin[pi(x - 1.4)] = 2sin(pi*x - 1.4pi)