Sinusoidal Function

Question

The pressure P (in pounds per square foot), in a pipe varies over time. Five times an hour, the pressure oscillates from a low of 40 to a high of 250 and then back to a low of 40. The pressure at time t=0 is 40. Let the function P=f(t) denote the pressure in pipe at time t minutes. Find a possible formula for the function P=f(t) described above. f(t)=

Answer 1

period = 1/5 of an hour

low = 40, high = 250

at time t=0 P=40

sinusoidal wave = P = f(t) = Asin(2pit/(1/5) + c) + D

where A = Amplitude = max -min all over 2 = 250-40)/2 = 210/2 = 105

D = mid line = max+min all over 2 = 290/2 = 145 = vertical shift

C = horizontal shift = -pi/2

B = 2pi/period = 2pi/(1/5) = 10pi

P = pressure = pounds per in^2 =

f(t) = 105sin(10pit -pi/2) + 145

at time t=0 P= 105sin(-pi/2) + 145 =105(-1) +145= 145-105= 40 lbs/in^2