Practice Final Problem 6 solution

Practice Final Problem 6 solution - (Spring 1997 The...

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(Spring 1997) The following problems deal with solving differential equations. You must use the Laplace transform or phasor methods to get credit for your solutions. The system has the transfer function ( ) 2 2 4 14 100 11 10 s s G s s s + + = + + . For c use ( ) 2 10 .7 1 5 5 1 1 1 10 s s G s s s + + =   + +     a) Give an analytical expression for the response to the excitation ( ) 2sin5 u t t = . (Reduce down to square roots and arc tangents of various quantities.) ( ) 2 2 100 4 14 10 11 j G j j ω - + = - + ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 100 4 14 10 11 G j - + = - + ( ) ( ) ( ) ( ) ( ) 2 2 2 2 5 100 100 70 70 1.228 225 3025 10 25 55 G j = - + = = = + - + ( ) ( ) ( ) 2 2 1 1 2 2 10 11 100 4 10 10 11 tan tan 100 4 10 G j j j - - = ∠ - + -∠ - + = - - - ( ) 1 1 0 0 0 5 70 55 tan tan 90 105.3 15.3
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