math245labprob02

# math245labprob02 - ω f (1 / 2 ≤ ω f ≤ 2), and plot...

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Math245 Computer assignment #2, Fall 2008 Consider the forced-damped 2nd-order system described by the equation: d 2 y dt 2 + 2 λω dy dt + ω 2 g ( y ) = f 0 sin ω f t. Case 1: Linear system Let g ( y ) = y . Choose ω = 1, λ = 1 / 8, f 0 = 1, y (0) = y 0 (0) = 0. 1. Simulate the response for ω f = 1 / 2, 1 and 2. Plot the response curve ( y vs. t ) and the phase portrait ( y 0 vs. y ) for each value of ω f . 2. For ω f = 1 / 2, 1, 2, ﬁnd the peak amplitude and the phase shift of the steady state response from the numerical solutions. Then, compare the peak amplitude and the phase shift with those obtained by the analytical prediction. To accomplish this task, complete following table for the peak amplitude and phase shift (you need to create one table for each). Analytical expression of the peak amplitude and the phase shift is found in Lab set #6. ω f Simulation Analysis 1/2 1 2 Case 2: Nonlinear system Let g ( y ) = sin y . Choose ω = 1, λ = 1 / 8, y (0) = y 0 (0) = 0. Simulate the response for f 0 = 0 . 1 and f 0 = 0 . 3 as a function of

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Unformatted text preview: ω f (1 / 2 ≤ ω f ≤ 2), and plot the peak amplitude of steady state response versus ω f for each value of f . (For example, see the following sketch. Similar problem is found in Example 2 in Lab set #6.) y peak ω f f = 0.1 f = 0.3 ?? 1 Related material Computer lab set #5 and #6. Work to be submitted Case 1 1. Plot of response curve and phase portrait for ω f = 1 / 2, 1, 2. 2. Comparison table for the peak amplitude and the phase shift (total two tables) . 3. Printout of Matlab ode function ﬁle and main program to do one of the cases in subprob-lem 1 ( ω f = 1 / 2 or 1 or 2) . Case 2 1. Plot of the peak amplitude diagram for f = 0 . 1 and 0.3 as sketched on the previous page. Separate plot for each value of f is acceptable. 2. Printout of Matlab ode function ﬁle and main program. 2...
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## This note was uploaded on 11/08/2009 for the course MATH 245 at USC.

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math245labprob02 - ω f (1 / 2 ≤ ω f ≤ 2), and plot...

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