CONCEPTS
(a) For an object in harmonic motion modeled by
(b) For an object in harmonic motion modeled by
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Algebra and Trigonometry (MindTap Course List)
- Blood Pressure The pressure P (in millimeters of mercury) against the walls of the blood vessels of a patient is modeled by P=10020cos8t3 where t is the time (in seconds). (a) Use a graphing utility to graph the model. (b) What is the period of the model? What does it represent in the context of the problem? (c) What is the amplitude of the model? What does it represent in the context of the problem? (d) If one cycle of this model is equivalent to one heartbeat, what is the pulse of the patient? (e) A physician wants the patient’s pulse rate to be 64 beats per minute or less. What should the period be? What should the coefficient of t be?arrow_forwardSKILLS 13-16. Simple Harmonic Motion Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time t=0. amplitude 6 in, frequency 5/ Hzarrow_forwardSimple Harmonic Motion A mass suspended from a spring oscillates in simple harmonic motion at a frequency of 4 cycles per second. The distance from the highest to the lowest point of the oscillation is 100 cm. Find an equation that describes the distance of the mass from its rest position as a function of time. Assume that the mass is at its lowest point when t=0.arrow_forward
- SKILLS 5-12. Simple Harmonic Motion The given function models the displacement of an object moving in simple harmonic motion. a Find the magnitude, period, and frequency of the motion. b Sketch a graph of the displacement of the object over one complete period. y=2sin3tarrow_forward47-54 Equations from a graph The graph of one complete period of a sine or cosine curve is given. a Find the amplitude, period, and horizontal shift. b Write an equation that represents the curve in the form. y=asinkx-b or y=acoskx-barrow_forwardCONCEPTS Objects A and B are in harmonic motion modeled by y=3sin2t- and y=3sin2t-2. The phase of A is _____________, and the phase of B is __________. The phase difference is ______________, so the objects are moving ______________ in phase/out of phase.arrow_forward
- Height of a Pole A 50-ft pole casts a shadow as shown in the figure. a Express the angle of elevation of the sun as a function of the length s of the shadow . b Find the angle of elevation of the sun when the shadow is 20 ft long.arrow_forwardAPPLICATIONS Strength of a Beam The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a log as in Exercise 67. Express the strength of the beam as a function of the angle in the figures.arrow_forwardPendulum A pendulum swings back and forth. The angular displacement of the pendulum from its rest position after t seconds is given by the function =20cos(3t). where is measured in degrees(Figure 14). a. Sketch the graph of this function for 0t6. b. What is the maximum angular displacement? c. How long does it take for the pendulum to complete one oscillation?arrow_forward
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