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Category > Computer Science Posted 08 Jan 2018 My Price 10.00

Solve analytically by separating variables and integrating

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MATLAB HW 

Thanks MAE 384. Advanced Mathematical Methods for Engineers. Homework Assignment 6. Due March 29. 1. Consider the di§erential equation: dy dt = 1 2 y sin2 t with initial condition given by y(0) = 1 Solve this equation from t = 0 to t = 10 using the following methods: (a) Solve analytically by separating variables and integrating. (b) Solve using the Euler implicit method. Use a time step size of 0.5. (c) Solve using the 4th-order Runge-Kutta method. Once again, use a time step size of 0.5. (d) Solve using the MATLAB function ode45. (e) Compare the results for the four methods. 2. A car and its suspension system traveling over a bumpy road can be modeled as a mass/spring/damper system. In this model, y1is the vertical motion of the wheel center of mass, y2 is the vertical motion of the car chassis, and y0 represents the displacement of the bottom of the tire due to the variation in the road surface. Spring/mass/damper model for an automobile suspension system. Applying Newtonís law to the two masses yields a system of second-order equations: m1y1 + c2( _y1 y_2) + k2(y1 y2) + k1y1 = k1y0 m2y2 c2( _y1 y_2) k2(y1 y2) = 0 (a) Convert the two second-order ODEís into a system of 4 Örst-order ODEís. Write them in standard form. (b) Assume the car hits a sharp bump in the road at t = 0 so that y0(t) = 8 < : 0:2t 0  t < 1 s 0:4 0:2t 1 < t < 2 s 0 t > 2 s Create a MATLAB function that returns the right hand sides of the equations derived in part (a) for an input t and input values of the displacements and velocities. (c) Solve the system on the time interval [0 30] seconds using the MATLAB function ode45. Find the displacement and velocity of the chassis and the wheel as a function of time. Use the following data: m1 = 70 kg, m2 = 1900 kg, k1 = 5000 N/m, k2 = 500 N/m, c2 = 600 N-s/m. Does this seem like a good design? 1

 

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SophiaPretty
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Status NEW Posted 08 Jan 2018 12:01 PM My Price 10.00

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