Question 1 (for loop) • Plot the response x(t) of an underdamped system with », = 2 rad/s,{ = 0.1,and v, = 0 for the following initial displacements: x, - 1 mm, x, - 5 mm, xo = 10 mm, and Xo = 100 mm. 0

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Question 1 (for loop)
Plot the response x(t) of an underdamped system with », = 2 rad/s, = 0.1, and vo = 0
for the following initial displacements: x, - 1 mm, x, - 5 mm, xo = 10 mm, and
Xo = 100 mm.
0 <t< 10 sec with 0.01 sec increment.
Put x-axis title, y-axis title, graph title and legend.
Note that:
The displacement for a free under-damped system:
x(t) = A e-3@nt sin(wat + 4)
(vo+ GwnXo)²+ (xo wa) ²
wa?
Where
A =
Xowd
$ = tan
vo + 3wnxo°
The damped natural frequency:
Wd = WnV1– {?
Transcribed Image Text:Question 1 (for loop) Plot the response x(t) of an underdamped system with », = 2 rad/s, = 0.1, and vo = 0 for the following initial displacements: x, - 1 mm, x, - 5 mm, xo = 10 mm, and Xo = 100 mm. 0 <t< 10 sec with 0.01 sec increment. Put x-axis title, y-axis title, graph title and legend. Note that: The displacement for a free under-damped system: x(t) = A e-3@nt sin(wat + 4) (vo+ GwnXo)²+ (xo wa) ² wa? Where A = Xowd $ = tan vo + 3wnxo° The damped natural frequency: Wd = WnV1– {?
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