Solve 2 matlab problems

Problem 1

A skydiver of mass m = 70 kg makes a high-altitude jump from a plane and wants to determine his maximum velocity. The differential equation of motion of the skydiver during the free fall can be derived by applying Newton’s second law which yields

[url removed, login to view] = mg-R (1.1)

Where v denotes the velocity, R is the aerodynamic drag force and g = 9.81 m/s^2 is the acceleration of gravity. The aerodynamic drag is proportional to the square of the velocity

R= av^2 (1.2)

Where a= 0.227 Ns^2/m^2.

Develop a MATLAB program to integrate numerically equation (1.1) over the time interval [0, tf] to find the maximum velocity of the sky-diver (you may need to experiment with the value of the final time tf to find the terminal velocity).

Determine also the acceleration of the sky-diver over the simulation time interval[0, tf]. Illustrate the results of your calculations by plotting the velocity and acceleration of the skydiver as a function of time. Discuss and critically appraise the results of your calculations.

Problem 2

A single degree of freedom model of a vehicle traveling at speed v over a rough road surface is shown in Figure 2 (a). The vehicle has a mass of m = 1500 kg, the suspension has a spring-damper system of a spring constant k = 400 kN/m and of a coefficient of viscous damping c = 2000 kg/s. The road surface varies harmonically (sinusoidally) with an amplitude Y = 0.02 m and a wavelength (the length of one cycle) of l =6 m.

The behaviour of the vehicle can be investigated by using a base vibration mode (see Figure 2 (b)). The vertical response (vibrations) x(t) of the vehicle are then governed by the second order differential equation of motion given as

mx .. (t) + cx sin cos Ω. (t) + kx (t) = kY sin Ωt + cYΩ cos Ωt (2.1)

Where Ω is the frequency of excitation due to the road surface given as

Ω = [1/ (3.6)] ([2 π *v]/l) (2.2)

Where the speed v is expressed in km/h.

Develop a MATLAB model (using an ode m-function and a relevant ode solver)) and a Simulink model to solve the equation of motion (2.1) and simulate the response the vehicle over the time interval [0, 20]s when it travels at two different speeds, 100 km/h and 55 km/h, respectively. Verify the correctness of your solution by comparing the results obtained from both models. Illustrate the results by plotting the vertical displacements the vehicle as a function of time. Discuss and critically appraise the simulation results, explaining why the vehicle is subject to different vibration levels at the two speeds.

Habilidades: Matlab and Mathematica

Ver mais: k-force, k force, find problems, 2 63 1, k to 12 program, x-plane, vibrations, solve, sin cos, simulink matlab, simulation models, simulation matlab, simulation in matlab, simulate matlab, ns-2, matlab/simulink, matlab simulink, matlab program, matlab problem, matlab find, MATLAB and SIMULINK, ky, kn, gravity model, CX

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( 1 comentário ) Daventry, United Kingdom

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I am a mechatronics engineering student in the german university in cairo. I am a senior, so this is my last year. I am very familiar with matlab & mathematics as I have worked with these softwares throughout 5 complet Mais

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