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# Tutorial 0.pdf - Math Revision 1 Simplifying the following...

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Math Revision 1. Simplifying the following fractions: (a) 9 s 2 s 9 5 s 1 2 (b) C B A 1 B A (c) D C B A 1 B A (d) 1 ) 1 s ( s 4 1 ) 1 s ( s 4 (e) s 1 25 s 4 s 25 1 25 s 4 s 25 2 2 (f) 1 ) B Js ( s k 1 ) B Js ( s k (g) h k 1 s k 1 1 s k (h) 1 s 1 kk 1 s k 1 s 1 kk 1 s k h h (i) 1 ) 1 Ts ( s k 1 ) 1 Ts ( s k 2. Determine roots for the following equations: (a) 0 6 x 5 x 2 (b) 0 5 x 2 x 2 (c) x 2 (x 2 +2x - 1) = 0 (d) x(x 3 + 6) - 1 = x 2 (x 2 + 1)

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3. Find the range of x for the following inequalities: (a) 4 x ) 2 x ( 4 (b) ) 1 x ( 3 x 2 12 (c) 0 k 3 4 ) 2 k ( k 3 0 k 3 (d) 0 k 5 20 0 k 5 (e) 0 k 10 0 k 2 4 4. Find Limits (a) s 1 k ) 1 Ts ( s k s 1 s lim 0 s (b) 2 2 0 s s 1 k ) B Js ( s k s 1 s lim 5. In a second order control system, when a unit step input is applied, the maximum overshoot and the peak time are given as % 100 e M 2 1 p  and 2 n p 1 t respectively. If the system has damping ratio = 0.3, and undamped natural frequency
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• Spring '14
• 3 sec, 2k, 1 sec

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