final_example - using Laplace transforms: (a) t 3 x d 3 dt...

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Inst tructor: Pr 1. Derive the fact draw th Am rofessor Gh the four-ter tors affectin he schematic merican U School Mec Final E haleb Husse rm equation ng this sprin c of the Spr University l of Engin chatronics xam Spri eini n for the vib ng including ring and sho y of Sharj neering s 500 ing 2005 Date: bration of a g a forced o ow all the fo jah May 24, 20 spring taki oscillation t orces that ar 005 ing into acc erm. Make re acting on 1 count all e sure to it.
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2 z za 2 2. Convert the following vectors to Cartesian coordinates: a cos - a sin (a) C = ρ φ + z θ (b) D = r cos sin a a 2 r 2 + r
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3 3. (a) Verify that A X V A) x V( (VA) X + = where V and A are scalar and vector fields, respectively. (b)Evaluate 1 . a cos sin a sin r a cos r A and r V when (VA) x r 2 φ θ φθ + + = =
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4 4. Using partial fraction expansion where required, find x (t) for a. X (s) = 4) 3)(s + + + 2)(s (s 1) ( + s s b. X (s) = 2 1) (s 4 + + s
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5 5. Find the complete time – domain solutions for the following differential equations
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Unformatted text preview: using Laplace transforms: (a) t 3 x d 3 dt e x 4 = + 0, dt 0, (0) x 2 dt with = = ) ( d dx(0) 2 x (b) 3t x(0) sin x 12-= = dt dx 6 6. Determine the inverse transform of 1) z-1)(z-(z 2 + 1) ( + z z by the following methods: (a) Partial fraction expansion. (b) Long division 7 7. Solve the wave equation (1) subject to the conditions: ) , ( , ) , ( = = t L u t u ) ( , ) ( x L x t u t − = ∂ ∂ u , x = = 8 4 10 5 3 ' ' ' ' ' ' = − + + y y y y 8. Find the general solution of 9 9. Find x 1 , x 2 , x 3 for the following system: 3x 1 + 2x 2 + x 3 =7 x 1 – x 2 + 3 x 3 = 3 5 x 1 + 4 x 2- 2 x 3 =1...
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final_example - using Laplace transforms: (a) t 3 x d 3 dt...

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