midterm_2_solu

midterm_2_solu - Name: ME 163 - Mechanical Vibrations...

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Unformatted text preview: Name: ME 163 - Mechanical Vibrations Second Midterm 50 points total, One 8.5 x 11 sheet of notes! Show all your work for full credit By signing your name you agree to the UCSB Honor Code Question 1 (10 pts) Consider the forced vibration system: 2 x ( t ) + 8 x ( t ) + 32 x ( t ) = u ( t ) 3pts: Perform the Laplace Transform of the left hand side of the equation. Do not assume that the initial conditions are zero. The Laplace transform is: 2( s 2 X ( s )- sx (0)- x (0)) + 8( sX ( s )- x (0)) + 32 X ( s ) 2pts: Perform the Laplace Transform of the right hand side of the equation. The Laplace transform is: U ( s ) 2pts: Let the initial conditions all equal zero and find the transfer function G ( s ) = X ( s ) U ( s ) By taking the ratio of the Laplace transform of the output over the input while initial conditions are zero reveals: X ( s ) U ( s ) = 1 2 s 2 + 8 s + 32 3pts: Consider the situation where the input u(t) is the Unit Impulse Function. Calculate x(t) for this using the Laplace Transform table which is included. You may consider the initial conditions as zero. The Laplace Transform of an impulse response is: U ( s...
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midterm_2_solu - Name: ME 163 - Mechanical Vibrations...

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