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Category | Programming |
---|---|

Subject | MATLAB |

Difficulty | Undergraduate |

Status | Solved |

More Info | Signal Processing Homework Help |

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- Parent Category: Programming Assignments' Solutions

SOLVED

Category | Programming |
---|---|

Subject | MATLAB |

Difficulty | Undergraduate |

Status | Solved |

More Info | Signal Processing Homework Help |

Assume a displacement sensor can be represented as a first-order system as follows
dy(t)
T
+ y(t) = bx(t)
dt
where x(t) represents displacement (mm), and y(t) represents the output (V). Assume all initial
conditions are zero.
=
a. Assume b 3. Calculate and plot from time t = 0 to t 30 seconds every 0.2 seconds the
response to a unit step increase in displacement when t = 1 and T = 5. Discuss the role of t
in the system's response and in determining the time constant.
b. Let x(t) = 1.0sin(2π0.1t). Calculate and plot the response to x(t) when t = 1 and t = 5.
Plot both the input x(t) and the output y(t) on the same panel. Discuss the role of t in the
system's response.

One could argue that a better representation of the displacement sensor is given by:
d²y(t) dy(t)
·+63· +9y(t) = 9x(t)
dt²
dt
a. Find and plot the response of the system above to a unit step increase in displacement when
= 0.3 and when = 0.707.
b. Let x(t) = 1.0 sin(2π0.1t). Calculate and plot the response to x(t) when 3 = 0.3 and when
<= 0.707. Discuss the apparent role of 3 in the system's response.
Let the input x (t) be the data in file "HWI_Q2.dat". Calculate and plot the response to x(t)
(data from file) when 3 = 0.3 and when 3 = 0.707. Calculate the mean squared error
between the input and the output for both values of 3. Discuss the apparent role of 3 in the
system's response.
C.

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