An object is attached to the end of a vibrating spring and its displacement from its equilibrium position is y = 8e-t/2sin 4t, where t is measured in seconds and y is measured in centimeters. a. Graph the displacement function together with the functions y = 8e-t/2 and y = -8e-t/2. How are these graphs related? b. Use the graph to estimate the maximum value of the displacement. Explain whether or not it occurs when the graph touches the graph of y = 8e-t/2. c. What is the velocity of the object when it first returns to its equilibrium position?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
An object is attached to the end of a vibrating spring and its displacement from its equilibrium position is y = 8e-t/2sin 4t, where t is measured in seconds and y is measured in centimeters.
a. Graph the displacement function together with the functions y = 8e-t/2 and y = -8e-t/2. How are these graphs related?
b. Use the graph to estimate the maximum value of the displacement. Explain whether or not it occurs when the graph touches the graph of y = 8e-t/2.
c. What is the velocity of the object when it first returns to its equilibrium position?
d. Use the graph to estimate the time after which the displacement is no more than 2 cm from equilibrium.
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