Trigonometric Functions (WORD PROBLEM)

plur222

New member
Joined
Mar 1, 2009
Messages
17
Consider the rhythm of your heartbeat. A person’s blood pressure is a measure of the pressure exerted on the walls of the arteries by the blood as it is propelled by the rhythmic contractions of the heart. Each time your heart beats, your blood pressure increases to a maximum value and then decreases to a minimum value as the heart rests between beats. The maximum and minimum blood pressure readings are called systolic and diastolic pressures, respectively. A blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered normal. A typical healthy person has a pulse rate of 70 heartbeats per minute.

What is the duration of one heartbeat in seconds? This represents the period of the blood pressure function.

Sketch the variation in pressure over the interval of one heartbeat. Start the graph with a pressure of 100mm at a time, t = 0 seconds.

What is the amplitude of this sinusoidal function? What does this value represent in the context of the patient’s blood pressure?

Since the phase shift of this function is zero, normal blood pressure can be expressed as a sinusoidal function of the form

P(t) = asin(bt) + d

Where t is time in seconds and p(t) is the pressure in mm of Hg.

Find a, b, and d and write the normal blood pressure function.
 
plur222 said:
Consider the rhythm of your heartbeat. A person’s blood pressure is a measure of the pressure exerted on the walls of the arteries by the blood as it is propelled by the rhythmic contractions of the heart. Each time your heart beats, your blood pressure increases to a maximum value and then decreases to a minimum value as the heart rests between beats. The maximum and minimum blood pressure readings are called systolic and diastolic pressures, respectively. A blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered normal. A typical healthy person has a pulse rate of 70 heartbeats per minute.

What is the duration of one heartbeat in seconds? This represents the period of the blood pressure function.

70 beats/min = 1/70 min/beat = 60/70 sec/beat or 6/7 sec for each beat

Sketch the variation in pressure over the interval of one heartbeat. Start the graph with a pressure of 100mm at a time, t = 0 seconds.

This would be a sinusoidal wave, with low point of 80 and high point of 120. The period is 6/7 sec.

What is the amplitude of this sinusoidal function? What does this value represent in the context of the patient’s blood pressure?

The amplitude would be 20. (120 - 100 or 100 - 80.)

Since the phase shift of this function is zero, normal blood pressure can be expressed as a sinusoidal function of the form

P(t) = a sin(bt) + d

Where t is time in seconds and p(t) is the pressure in mm of Hg.

Find a, b, and d and write the normal blood pressure function.

a = 20
b = 1/(6/7) = 7/6
d = 100

P(t) = 20 sin (6t/7) + 100
 
P(t) = A sin (?t + ?) + d

T = 6/7 sec

? = 2?/T = 7?/3

? = 0

A = 20

d = 100
 
Top