test301-2-f09

test301-2-f09 - The force or input u is applied to mass m 2...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
A-AE 301 exam two, fall 2009. Please put your best answer clearly written on the exam in a box. Two page of notes and no calculators. NAME: 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 1. Solve the following difierential equation where the initial conditions are all zero _ y + y = 5 cos(2 t ) : y ( t ) = 2
Background image of page 2
Problem 2. Compute e At for A = 2 4 ¡ 2 2 ¡ 4 2 3 5 : e At = 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 3. Compute the transfer function for the following state space system 2 4 _ x 1 _ x 2 3 5 = 2 4 ¡ 2 ¡ 1 1 0 3 5 2 4 x 1 x 2 3 5 + 2 4 2 0 3 5 u y = h 1 1 i x 3a) The transfer function is G ( s ) = Y ( s ) U ( s ) = 3b) The impulse response g ( t ) for this system is given by g ( t ) = 4
Background image of page 4
Problem 4. Consider the transfer function Y ( s ) U ( s ) = G ( s ) = 8476 s 3 + 274 s 2 ¡ 37628 s + 4 ( s 2 + 9789 s + 1)( s 2 + 321 s + 2) Assume that the input u ( t ) = 12. Then flnd lim t !1 y ( t ) = 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 5. Construct a circuit consisting of a resistor, capacitor and inductor whose transfer function is given by G ( s ) = 2 s 2 2 s 2 + s + 1 : 6
Background image of page 6
Problem 6. Design a circuit in Simulink using integrators, summers and gains for the transfer function G ( s ) = 3 s + 1 s 2 + s + 4 : 7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Problem 7. Find the transfer function for the state space system: _ x = 2 6 6 6 6 6 6 4 0 1 0 0 0 0 1 0 0 0 0 1 ¡ 10 ¡ 20 ¡ 30 ¡ 40 3 7 7 7 7 7 7 5 x + 2 6 6 6 6 6 6 4 0 0 0 1 3 7 7 7 7 7 7 5 u y = h 1 2 3 0 i x Y ( s ) U ( s ) = G ( s ) = 8
Background image of page 8
Figure Problem 8 Problem 8. Consider the mass spring damper system in Figure 8.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The force or input u is applied to mass m 2 . The distance from the ±oor to m 2 is x 2 , while the distance from the ±oor to m 1 is x 1 . Moreover, m 1 = m 2 = 1 ; k 1 = k 2 = 1 and c = 1 : Find the transfer function from u to the output y = x 1 . Y ( s ) U ( s ) = G ( s ) = 9 i u y Z 1 Z 2 Figure Problem 9 Problem 9. Find the transfer function with the input u and output voltage y for the circuit given in the Figure for Problem 9 where Z 1 is a resistor R 1 = 1 and a capacitor C = 1 in parallel, while Z 2 consists of a single resistor R 2 = 1. 10 Laplace transform pairs g ( t ) G ( s ) = R 1 e ¡ st g ( t ) dt – ( t ) 1 1 1 =s t n n ! =s n +1 e at 1 = ( s ¡ a ) cos( !t ) s= ( s 2 + ! 2 ) sin( !t ) != ( s 2 + ! 2 ) e at t n n ! = ( s ¡ a ) n +1 e at cos( !t ) ( s ¡ a ) = (( s ¡ a ) 2 + ! 2 ) e at sin( !t ) != (( s ¡ a ) 2 + ! 2 ) 11...
View Full Document

This document was uploaded on 12/29/2011.

Page1 / 11

test301-2-f09 - The force or input u is applied to mass m 2...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online