Question

point) The pressure P (in pounds per square foot), in a pipe varies over time. Four times an hour, the pressure oscillates from a low of 40 to a high of 300 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.

Answer 1

mean = 340/2 = 170
amplitude = 300-170 = 130
min at t = 0 so
y = 170 - 130 cos(w t) which is 40 at t = 0
what is w?
when t = 15 min , w t = 2 pi
so
w 15 = 2 pi
w = (2/15) pi
so
y = 170 - 130 cos(2 pi t/15)