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Two masses are attached to a wall by linear springs (see the d²x1 ki k2 +('7 – Ix)- –(x2 – X1 – wi – L2)

Two masses are attached to a wall by linear springs (see the d²x1 ki k2 +('7 – Ix)- –(x2 – X1 – wi – L2)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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L k X2 Two masses are attached to a wall by linear springs (see the Figure above). Force balancing based on Newton's second law leads to the following equations: d²x1 k2 -(x) - L) + (x2 m1 - x¡ – wj - L2) dt2 d²x2 dt² k2 (x2 - X - uw – L2) m2 Here k1 and k2 are spring constants, m1 and m2 are masses and w1 and w2 are their widths. L1 and L2 are the un-stretched lengths of the springs. (a) Solve the above differential equations any of the ODE solvers available in MATLAB/Octave from t = 0 to 50 (b) Construct the time series plots of x1 and x, and their derivatives. (x1 and x2 versus time in one plot, v1 and v2 versus time in another plot) (c) Construct phase-plane plot between x, and x2 (x1 versus x2). Use the following parameters (in arbitrary units): k1 = k2 = 5; m1=m2 = 2 W1 = w2 = 5; L1= L2 = 2 Initial Conditions: X1 = L1 and x2 = L1 + w1+ L2+ 6.
Transcribed Image Text:L k X2 Two masses are attached to a wall by linear springs (see the Figure above). Force balancing based on Newton's second law leads to the following equations: d²x1 k2 -(x) - L) + (x2 m1 - x¡ – wj - L2) dt2 d²x2 dt² k2 (x2 - X - uw – L2) m2 Here k1 and k2 are spring constants, m1 and m2 are masses and w1 and w2 are their widths. L1 and L2 are the un-stretched lengths of the springs. (a) Solve the above differential equations any of the ODE solvers available in MATLAB/Octave from t = 0 to 50 (b) Construct the time series plots of x1 and x, and their derivatives. (x1 and x2 versus time in one plot, v1 and v2 versus time in another plot) (c) Construct phase-plane plot between x, and x2 (x1 versus x2). Use the following parameters (in arbitrary units): k1 = k2 = 5; m1=m2 = 2 W1 = w2 = 5; L1= L2 = 2 Initial Conditions: X1 = L1 and x2 = L1 + w1+ L2+ 6.
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