Simple Harmonic Motion: A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from the origin at time t is given by either the sine or cosine function. 1) A buoy oscillates in simple harmonic motion as waves go past. It is noted that the buoy moves a total of 3.5 feet from its low point to its high point, and that it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy if its high point is at t=0.
2) A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches. Its motion is modeled by y= (t>0), where y is measured in feet and t is time in seconds. a) What is the period? b) Determine the first time the weight passes the point of equilibrium (y=0).
3) A Ferris wheel is built such that the height h (in feet) above ground of a seat on the wheel at time t (in seconds) can be modeled by ( ) ( ) a) Find the period of the model. What does the period tell you in terms of the ride?
b) Find the amplitude of the model. What does the amplitude tell you about the ride?
c) How long would it take to complete 5 revolutions around?
4) The function given by P=100 – 20cos approximates the blood pressure P (in millimeters) of mercury at time t (in seconds) for a person at rest. a) Find the period of the function. b) Find the number of heartbeats per minute.
5) For the past three years, the manager of The Christmas Barn has observed that revenue reaches a high of about $40,000 in December and a low of about $10,000 in June, and that the graph of the revenue looks periodic (like sine or cosine!!). The months are numbered 1 through 36 with 1 corresponding to January. a) Find the amplitude, vertical shift, period, and phase shift for a cosine curve modeling this situation. Write the equation.
b) Find the amplitude, vertical shift, period, and phase shift for a sine curve modeling this situation. Write the equation.
c) Use both equations from above to predict the approximate revenue for April.
A point that moves on a coordinate line is said to be in simple ...
a) Find the period of the model. What does the period tell you in terms of the ride? b) Find the amplitude of the model. What does the amplitude tell you about the ...
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A valid driver's license is required. Personal vehicles are helpful but not required. Responsibilities: Work independently to collect biotic and abiotic data in field ...
For more information: http://forestecology.cfans.umn.edu/Research/B4WARMED/. Position overview: We seek undergraduate or newly graduated students with a ...
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