CONCEPTS
Objects A and B are in harmonic motion modeled by
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Chapter 6 Solutions
Algebra and Trigonometry (MindTap Course List)
- CONCEPTS For an object in simple harmonic motion with amplitude a and period 2/, find an equation that models the displacement y at any time t if a y=0 at time t=0: y= ____________. b y=a at time t=0: y= ____________.arrow_forwardAPPLICATIONS A Bobbing Cork A cork floating in a lake is bobbing in simple harmonic motion. Its displacement above the lake is modeled by y=0.2cos20t+8 Where y is measured in meters and t is measured in minutes. a Find the frequency of the motion of the cork. b Sketch a graph. c Find the maximum displacement of the cork above the lake bottom.arrow_forwardHOW DO YOU SEE IT? The graph below shows the displacement of an object in simple harmonic motion. (a) What is the amplitude? (b) What is the period? (c) Is the equation of the simple harmonic motion of the form d=asintord=acost?arrow_forward
- CONCEPTS a For an object in harmonic motion modeled by y=Asinkt-b the amplitude is ________________, the period is _______________, and the phase is _____________. To find the horizontal shift, we factor out k to get y=_______________. From this form of the equation we see that the horizontal shift is ______________. b For an object in harmonic motion modeled by y=5sin4t- the amplitude is ________________, the period is _______________, and the phase is _____________ and the horizontal shift is _______________.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_forwardSKILLS 17-20. Simple Harmonic Motion Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t=0. amplitude 60 ft, period 0.5 minarrow_forward
- View from a Satellite The figures on the next page indicate that the higher the orbit of satellite, the more of the earth the satellite can see. Let ,s, and h be as in the figure, and assume that the earth is a sphere of radius 3960 mi. a Express the angle as a function of h. b Express the distance s as a function of . c Express the distance s as a function of h. Hint: Find the composition of the functions in parts a and b. d If the satellite is 100 mi above the earth, what is the distance s that it can see? e How high does the satellite have to be to see both Los Angeles and New York, 2450 mi apart?arrow_forwardSKILLS 17-20. Simple Harmonic Motion Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is at its maximum at time t=0. amplitude 6.25 in., frequency 60 Hzarrow_forwardSKILLS 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_forward
- Simple 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_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_forward
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