Question

The pressure P (in pounds per square foot), in a pipe varies over time. Ten times an hour, the pressure oscillates from a low of 40 to a high of 280 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 the formula for the function P=f(t),

Answer 1

Pressure oscillating ten times every hour. So period n = 6 min. So the negative cos is represented in the graph and since it datrt at time 0, P = f(t) = Acos(Bt) + D Amplitude A = (Ph - Pl) / 2 = (280 - 40) / 2 = 240 / 2 = 120 Period B = 2xpi / 6 = pi /3 D = (Ph + Pl) / 2 = (280 + 40) / 2 = 320 / 2 = 160 Subtituting the equation we get f(t) = 120cos (pi x t ) / 3 + 160.