The pressure, P, (inlbs/ft^2) in a pipe varies over time. Five thimes anhour, the pressure oscillates from a low of 90 to a high of230 and then back down to 90. The pressure at t = 0 is 90. a) graph P = f(t) where t is time inminutes. label axes. b) find a possible formulatfor P= f(t) c) by graphing P = f(t) for 0 (isless than or equal to) t ( less than or equal to) 2, estimate whenthe pressure first equals 115 lbs/ft^2

Question

The pressure,

P, (i n l b s / f t^{2})

in a pipe varies over time. Five thimes anhour, the pressure oscillates from a low of 90 to a high of230 and then back down to 90. The pressure at t = 0 is 90.
a) graph P = f(t) where t is time inminutes. label axes.
b) find a possible formulatfor P= f(t)
c) by graphing P = f(t) for 0 (isless than or equal to) t ( less than or equal to) 2, estimate whenthe pressure first equals

115 l b s / f t^{2}

Answer 1

Firstly, You should use a sin graph because of the oscillations.The function should be in the form

f (t) = a \cos ((2 π / b) t) + C

Since your graph is increasing it must be -a because normally a cosgraph is at its max at 0 and not its min.
a is the amplitude ( this is the difference between the max and themin divided by 2)
b is the frequency( the number of times the graph repeats itselfwithin

2 π

)

= 10 π

2 π / b

equals the frequency (that is the cycle in which the graphrepeats itself)(since you said 5 times at t = 1, the period is.2)
c is the vertical shift. (in this case it would be 90 sincenormally it would be 0 but the graph has been shifted 90 up) t is the time

f (t) = - 70 \cos (.2 t) + 90

Answers (1)

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