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3. A spring mass system with friction has mass m = 2 kg, friction constant a = 4 kg/sec, and Hooke's constant k = 6 kg/sec?. The spring mass system has 2nd order homoge- neous differential equation given by the following: yl" + 2y' + 3y = 0, y(0) = 2 m, y' (0) = 3 m/sec (a) Write the down the differential matrix equation for the corresponding system of first order ODES and find the eigenvalues. (b) Find the eigenvectors corresponding to each of the eigenvalues. (c) Find the general solution, 7(t), using the given initial conditions.

3. A spring mass system with friction has mass m = 2 kg, friction constant a = 4 kg/sec, and Hooke's constant k = 6 kg/sec?. The spring mass system has 2nd order homoge- neous differential equation given by the following: yl" + 2y' + 3y = 0, y(0) = 2 m, y' (0) = 3 m/sec (a) Write the down the differential matrix equation for the corresponding system of first order ODES and find the eigenvalues. (b) Find the eigenvectors corresponding to each of the eigenvalues. (c) Find the general solution, 7(t), using the given initial conditions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve b and c thoroughly Answers should look something like this
3. (a) A = -1+ iv2, 2 = -1 – iv2 =l- (b) v1 = 3 V2 = [=l+iv2 (c) 7() = (") | el-1+ivZjt + (19N el-1-iv)t 1 3 3 4
Transcribed Image Text:3. (a) A = -1+ iv2, 2 = -1 – iv2 =l- (b) v1 = 3 V2 = [=l+iv2 (c) 7() = (") | el-1+ivZjt + (19N el-1-iv)t 1 3 3 4
3. A spring mass system with friction has mass m = 2 kg, friction constant a = 4 kg/sec, and Hooke's constant k = 6 kg/sec?. The spring mass system has 2nd order homoge- neous differential equation given by the following: yl" + 2y' + 3y = 0, y(0) = 2 m, y' (0) = 3 m/sec (a) Write the down the differential matrix equation for the corresponding system of first order ODES and find the eigenvalues. (b) Find the eigenvectors corresponding to each of the eigenvalues. (c) Find the general solution, (t), using the given initial conditions.
Transcribed Image Text:3. A spring mass system with friction has mass m = 2 kg, friction constant a = 4 kg/sec, and Hooke's constant k = 6 kg/sec?. The spring mass system has 2nd order homoge- neous differential equation given by the following: yl" + 2y' + 3y = 0, y(0) = 2 m, y' (0) = 3 m/sec (a) Write the down the differential matrix equation for the corresponding system of first order ODES and find the eigenvalues. (b) Find the eigenvectors corresponding to each of the eigenvalues. (c) Find the general solution, (t), using the given initial conditions.
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