Periodic Functions Worksheet



Periodic Functions Worksheet

1.) What values of a, b, d are needed to give a sine wave function f(x) = a sin(bx) + d with:

a.) max value120, min value 80, period 60 b.) max value 101, min value 98, period 24

c.) max value 5, min value 3, period 1.5

2.) A simplified model of respiration gives the rate of air flow into the lungs v (in liter/sec) as a function of time t (sec) (starting with the beginning of a breath) as v(t) = .5sin.

a.) sketch the graph of this function - show at least two complete cycles - and use it to answer b - e.

b.) What is the length of time for each breath in this model?

c.) How long is spent inhaling during each breath?

d.) What is the maximum rate of flow into the lungs and when does it occur?

e.) When does the maximum flow out of the lungs occur?

3.) In a simplified model of blood pressure in an artery, the pressure (pressure above atmospheric pressure) varies from 80 torr (the diastolic reading) to 120 torr (the systolic reading) during each beat, following a sine wave. If the pulse rate is 80 beats/min (so that the period for each beat is 1/80 min, or .75 sec), the pressure in the artery at time t seconds (t=0 represents the beginning of muscle contraction in the heart) is be given in this model by

P(t) = 20sin + 100

a.) Sketch the graph of this function (show at least two cycles)

b.) When is the pressure greatest?

c.) If the pulse rate is 100 beats/min, what is the function for pressure? Sketch the graph.

d.) If the diastolic pressure is 140 torr (but systolic remains at 80 torr and pulse rate remains at 80 beats/min) give the function for P(t). Sketch the graph.

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