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. Six times an hour, the pressure oscillates from a low of 60 to a high of 240 and then back to a low of 60. The pressure at time t=0 is 60. 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 = 60/6 = 10 minutes

amplitude = (240 -60)/2 = 90 ; It is given at t= 0 P(t)= 60

So, P(t) = 150 - 90cos(2pi/10*t)

P(t) = 150 -90cos(pi*t/5)

we can check at t=0 P(0) = 150 -90*1 = 60

This equation holds true