Phase and Phase Difference A pair of sine curves with the same period is given. (a) Find the phase of each curve. (b) Find the phase difference between the curves. (c) Determine whether the curves are in phase or out of phase. (d) Sketch both curves on the same axes.
56.
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Bundle: Precalculus: Mathematics for Calculus, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's Precalculus, Enhanced Edition, 7th Edition, Single-Term
- Harmonic Motion The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t)=12cos6t where y is the displacement in feet and t is the time in seconds. Find the displacement when (a) t = 0, (b) t=14, and (c) t=12.arrow_forwardThe sine curves y1=30sin(6t2) and y2=30sin(6t3) have the same period. a Find the phase of each curve. b Find the phase difference between y1 and y2. c Determine whether the curves are in phase or out of phase. d Sketch both curves on the same axes.arrow_forwardOscillating Spring A mass attached to a spring oscillates upward and downward. The displacement of the mass from its equilibrium position after t seconds is given by the function d(t)=3.5cos(2t), where d is measured in centimeters (Figure 12). Find all times at which the displacement is zero.arrow_forward
- The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t)=3sin(t/4), where y is the displacement in feet and t is the time in seconds. Complete the table Use the table feature of a graphing utility to determine when the displacement is maximum. Use the table feature of the graphing utility to approximate the time t (0 < t < 8) when the weight reaches equilibrium.arrow_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_forwardOscillation of a Spring A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches. Its motion (in ideal conditions) is modeled by y=14cos16t,t0, where y is measured in feet and t is the time in seconds. (a) Graph the function. (b) What is the period of the oscillations? (c) Determine the first time the weight passes the point of equilibrium y=0.arrow_forward
- Motion of a Projectile If a projectile (such as a bullet) is fired into the air with an initial velocity v at an angle of elevation (see Figure 10), then the height h of the projectile at time t is given by h=16t2+vtsin Give the equation for h, if v is 600 feet per second and is 45. (Leave your answer in exact value form.)arrow_forwardBlood 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_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage