# S1 - EE 2200 Spring 2010 Section ONE 1 ECE 2200 Spring 2010...

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EE 2200 / Spring 2010: Section ONE 1 ECE 2200 / Spring 2010 SECTION ONE (Week 2: Feb 1-4) 1. Find the cyclic frequency, radian frequency, period, phase shift, and amplitude of the following signals (i) x ( t ) = 6 . 5 cos(2 π 420 t - π/ 3) (ii) y ( t ) = 11 cos(0 . 2 π ) cos(157( t + 0 . 02)) (iii) z ( t ) = (3 + 2 j )(3 - 2 j ) cos(370 πt + 0 . 7 π ) 2. Simplify the following expressions by putting them in the form Ae (i) 3 e j π 2 + 4 e - j π 3 (ii) ( 2 - j 5) 10 (iii) ( 3 - j 3) - 1 (iv) Re { je - π 6 } 3. Using phasor algebra, simplify x ( t ) = 5 cos( ωt ) + 10 cos( ωt + π 3 ) + 15 cos( ωt + 7 π 6 ) into the standard form A cos( ωt + φ ) by determining A and φ . 4. Given w ( t ) = 1 . 5 cos(2 π 5 t ), sketch the following signals (i) x ( t ) = w ( t - 1 30 ) (ii) y ( t ) = w ( t + 1 15 ) (iii) z ( t ) = [2 w ( t + 1 10 )] 2 5. Consider relating the phase shift φ of a sinusoid to a time shift t 1 implicit in x ( t ) = A cos(2 πf 0 t + φ ) = A cos(2 πf 0 ( t - t 1 )) Assume that the period of x ( t ) is T 0 = 64 msec, detemine the value of the phase φ in radians when (i) t 1 = - 16 msec (ii) t 1 = 24 msec (iii) t 1 = 56 msec

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EE 2200 / Spring 2010: Section ONE 2 6. Consider an unforced, undamped second order differential equation, such as that
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