MATLAB Experiments-2(ccm)

Experiment 2---MATLAB Plotting 1. Position and velocity of a Ball If a stationary ball is released at a height above the surface of the Earth with a vertical velocity ,the position and velocity of the ball as a function of time will be given by the equations where g is the acceleration due to gravity(-9.81 ), h is the height above the surface of the Earth (assuming no air friction), and v is the vertical component of velocity. Write a MATLAB program that prompts a user for the initial height of the ball in meters and velocity of the ball in meters per second. and plots the height and velocity as a function of time. Be sure to include proper labels in your plots. (The initial velocity:20m/s; the initial height: 10 m. calculate the speed and height for the first 10 seconds of flight. put legends on the figure)        2.  Radio Receiver The resonant frequency of the LC circuit is given by the equation (1) (1) The average (rms) voltage across the resistive load in Figure 2 varies as a function of frequency according to Equation (2) (2) where and is the frequency in hertz. Assume that L=0.25mH, C=0.10nF, , and . (a) Calculate the resonant frequency of the LC circuit. (b) Plot the rms voltage on the resistive load as a function of frequency. At what frequency does the voltage on the resistive load peak? What is the voltage on the load at this frequency? (c) If the frequency is changed to 10% greater than the resonant frequency, what is the voltage on the load? Figure 2 3. Output Power from a Motor: The output power produced by a rotating motor is given by the equation (3) where is the induced torque on the shaft in newton-meters, is the rotational speed of the shaft in radians per second, and P is in Watts. Assume that the rotational speed of a particular motor shaft is given by the equation (4) and the induced torque on the shaft is given by (5) Use three subplots to plot the torque, speed, and power supplied by this shaft versus time for . Be sure to label your plot properly with the symbols and where appropriate. Use 2-point-wide solid blue line and the font of labels should be bold face. The final figure should look like figure 3. Figure 3 4. Plotting Orbits: When a satellite orbits the Earth, the satellite's orbit will form an ellipse with the Earth located at one of the focal points of the ellipse. The satellite's orbit can be expressed in polar coordinates as (6) where r and are the distance and angle of the satellite from the center of the Earth, p is a parameter specifying the size of the orbit, and is a parameter representing the eccentricity of the orbit. A circular orbit has an eccentricity of 0. An elliptical orbit has an eccentricity of . If , the satellite follows a hyperbolic path and escapes from the Earth's gravitational field. Consider a satellite with a size parameter p=1000 km. Plot the orbit of this satellite if (a) =0; (b) =0.25; (c) =0.5. How close does each orbit come to the Earth? How far away does each orbit get from the Earth? Compare the three plots you created. Can you determine what the parameter p means from looking at the plots?