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Unformatted text preview: ME163 Mechanical Vibrations (Winter 2009) HW-1 Due 1.15.08 in class-25% if late within 24 hours-50% if later than that 1. This problem is a review of some necessary background from mathematics. Consider the following differential equation ¨ x ( t ) + 2 ˙ x ( t ) + 2 = ˙ y ( t ) + 2 Such equation are often solved by taking the Laplace transform of the input y ( t ) and output x ( t ) which is defiend as follow X ( s ) = integraldisplay ∞ e- st x ( t ) dt Y ( s ) = integraldisplay ∞ e- st y ( t ) dt where s is a complex number. Take the Laplace transform of both sides of the equation with x (0) = ˙ x (0) = 0 ,y (0) = 0 to obtain X ( s )( s 2 + 2 s + 2) = Y ( s )( s + 2) Divide X ( s ) by Y ( s ) to obtain a quantity called the Transfer Function H ( s ). H ( s ) = X ( s ) Y ( s ) = s + 2 s 2 + 2 s + 2 Later we will see that it determines how the output x ( t ) depends on the input y ( t ).We shall see more about H ( s ) later in the course, for now we would like to play with complex number • We call the roots of the polynomial in the numerator of the transfer functin as zeors and that of the denominator as poles . Find the zeros and poles of the transfer function.....
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This note was uploaded on 03/23/2009 for the course ME 163 taught by Professor Mezic,i during the Winter '08 term at UCSB.
- Winter '08