MEC702_Wk_10_Tutorial

# MEC702_Wk_10_Tutorial - MEC702 Wk 10 Tutorial Critical...

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Unformatted text preview: MEC702 Wk 10 Tutorial Critical Points. Stability. Exercise. Determine the type of critical point and its stability as well. a.) y10 = y1 b.) y20 = 2y2 c.) y10 = −4y1 y20 = −3y2 y10 = y2 d.) y10 = 2y1 + y2 y20 = −9y1 y20 = 5y1 − 2y2 Laplace Transform Exercise. Find the transform L (f ). Assume a, b, ω are constants. (a − bt)2 a.) 3t + 12 b.) c.) cos πt d.) e2t sinh t Given F (s) = L (f ), nd f (t) where a, b, L, n are constants. 5s + 1 0.2s + 1.8 b.) s2 + 3.24 s2 − 25 12 228 s + 10 − 6 d.) s4 s s2 − s − 2 Exercise. a.) c.) Derive the Laplace transform for the functions f (t) = eat sin ωt and g(t) = e cos ωt. (Hint: Use s-Shifting) Exercise. at IVPs Exercise. Solve the IVPs by the Laplace transform. Show all details. a.) y 0 + 5.2y = 19.4 sin 2t, b.) 0 y + 2y = 0, 0 y(0) = 1.5 c.) y − y − 6y = 0, y(0) = 11 y 0 (0) = 28 d.) y 00 + 9y = 10e−t , 1 y 00 − y = 0, 4 y(0) = 0 y 0 (0) = 0 y(0) = 12 y 0 (0) = 0 e.) 00 y(0) = 0 1 ...
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