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# HW10 - θ 2 Use g = 9 81 m/s 2 and l = 0 5 m Apply three...

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EMAE 250: Homework 10 April 7, 2011 1. Given dy dx = - 15(sin x + y ) - cos x (a) [1pt] If y (0) = 1, use the explicit Euler’s method to obtain a solution from x = 0 to x = 1 with the step size, h = 0 . 5 . (b) [1pt] For the same initial values, use the implicit Euler’s method to obtain a solution from x = 0 to x = 1 with h = 0 . 5. 2. [3pt] Consider the inverted pendulum shown in Lecture-Week 11, p12. If the mass- less rod is ﬁxed with a rotational joint and the mass, m , is concentrated on the other end. For a small value of θ , this system can be solved using d 2 θ dt 2 - g l θ = 0 For θ 0 = θ (0) = 0, (0) dt = 0 . 25[rad/s] and h = 0 . 1, ﬁrst apply Heun’s method to solve the next point and then apply the non-self-starting Heun’s method to compute
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Unformatted text preview: θ 2 . Use g = 9 . 81 m/s 2 and l = 0 . 5 m . Apply three correctors and compute the relative fractional relative error, ± a . 3. For the following matrix: A = 44 9-6 280 57 40 75 15 13 (a) [1pt] Compute the eigenvalues of A analytically. (b) [2pt] Find the dominant eigenvalue of A by using the power method. Perform 3 iterations. Find three eigenvalues of A by using ‘eig(A)’ function in Matlab and compare the results. (c) [2pt] Find the second dominant eigenvalue of A by using the power method after deﬂation. Perform 3 iterations. 1...
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