# (Solved) : Shock Absorbers Damp Oscillations Car Hit Pothole Cars Normally Signty Underdamped Bounce Q42700859 . . .

Python question
Shock absorbers damp the oscillations in your car after you hit a pothole. Cars normally are signty underdamped – you bounce a time or two after hitting a pothole. Underdamped oscillations The equation below describes underdamped oscillations where x is the displacement of the object of interest at time t relative to some initial position Xo at time to = 0; x(t) = *We-ft cos(yt – ) where xow,ß are parameters (all are floating point values), y = /w2 – B2, and p = tan-(B/y). The names of the Greek letters used in the equation are: w omega, Y gamma, ß beta, and phi. Write a program that asks the user to input the values for Xo, w,ß, and final and then plots a smooth curve x(t) on the interval [0, trinali.e. the number of points plotted should capture the oscillations. In addition, add code to highlight where the displacement x is negative: that is, plot all negative values of x again but now designate these points with an asterisk (or a circle). The smooth curve must be of color blue; the asterisks (or circles) must be of color red. Include a meaningful title and labels for the axes (we are omitting units in this problem). You may assume that the user inputs valid values for Xo,w, B, and Trinal You can (and should use the numpy and matplotlib.pyplot packages but you cannot use other packages such as sympy. Recall that the functions cos(), exp(),sqrt(), and arctan () are available in the numpy module. Show transcribed image text Shock absorbers damp the oscillations in your car after you hit a pothole. Cars normally are signty underdamped – you bounce a time or two after hitting a pothole. Underdamped oscillations The equation below describes underdamped oscillations where x is the displacement of the object of interest at time t relative to some initial position Xo at time to = 0; x(t) = *We-ft cos(yt – ) where xow,ß are parameters (all are floating point values), y = /w2 – B2, and p = tan-(B/y). The names of the Greek letters used in the equation are: w omega, Y gamma, ß beta, and phi. Write a program that asks the user to input the values for Xo, w,ß, and final and then plots a smooth curve x(t) on the interval [0, trinali.e. the number of points plotted should capture the oscillations. In addition, add code to highlight where the displacement x is negative: that is, plot all negative values of x again but now designate these points with an asterisk (or a circle). The smooth curve must be of color blue; the asterisks (or circles) must be of color red. Include a meaningful title and labels for the axes (we are omitting units in this problem). You may assume that the user inputs valid values for Xo,w, B, and Trinal You can (and should use the numpy and matplotlib.pyplot packages but you cannot use other packages such as sympy. Recall that the functions cos(), exp(),sqrt(), and arctan () are available in the numpy module.

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