The pressure P in pounds per square foot in a pipe varies ov

The pressure P (in pounds per square foot), in a pipe varies over time. Three times an hour, the pressure oscillates from a low of 90 to a high of 250 and then back to a low of 90. The pressure at time t=0 is 90. 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.

Solution

pressure P (in pounds per square foot), in a pipe varies over time

Its a sinusoidal function

period = 60/3 = 20 minutes

B= 2pi/20 = pi/10

amplitude = (250 -90)/2 = 80 ; It is given at t= 0 P(t)= 90

So, P(t) = 170 - 80cos(pi/10*t)

P(t) = 170 -90sin(pi*t/5)