1 Free Vibration Response of Single Degree of Freedom System(100 %) 1 Figure 1 represent a simple vibration system. The free vibration response of an undamped single degree of freedom (SDOF) oscillator is given by its displacement x(t) satisfying 1(t) = 1(0)sin*(wt)e-2dut + v(0) 2cos(wt)e-10dwt (1) where t is time in seconds and w = Vis the natural frequency of the system with m and k being the mass and the stiffness of the system. d is the damping coefficient of the system. Define v(t) and a(t) as the time dependent velocity and acceleration of the system. Write an M-file script using functions that will compute and plot 1. The displacement of the system r(t) over time 2. The velocity of the system v(t) over time 3. The acceleration of the system a(t) over time for three damping coefficients (d = 0,1,5) within a time interval 0 < t < 10 s. You will need THREE(3) functions, one for each displacement, velocity and acceleration calculations. Assume m = 10, k = 1 and that x(0) = v(0) = 10. Note that r(t), v(t), a(t) should be on ONE plot for each damping coefficient. Use the a solid line for the displacement, broken-lines for the velocity and dotted lines for acceleration. Thus, your code needs to produce THREE plots (one for each damping coefficient) for comparison. Please use the subplot command.
1 Free Vibration Response of Single Degree of Freedom System(100 %) 1 Figure 1 represent a simple vibration system. The free vibration response of an undamped single degree of freedom (SDOF) oscillator is given by its displacement x(t) satisfying 1(t) = 1(0)sin*(wt)e-2dut + v(0) 2cos(wt)e-10dwt (1) where t is time in seconds and w = Vis the natural frequency of the system with m and k being the mass and the stiffness of the system. d is the damping coefficient of the system. Define v(t) and a(t) as the time dependent velocity and acceleration of the system. Write an M-file script using functions that will compute and plot 1. The displacement of the system r(t) over time 2. The velocity of the system v(t) over time 3. The acceleration of the system a(t) over time for three damping coefficients (d = 0,1,5) within a time interval 0 < t < 10 s. You will need THREE(3) functions, one for each displacement, velocity and acceleration calculations. Assume m = 10, k = 1 and that x(0) = v(0) = 10. Note that r(t), v(t), a(t) should be on ONE plot for each damping coefficient. Use the a solid line for the displacement, broken-lines for the velocity and dotted lines for acceleration. Thus, your code needs to produce THREE plots (one for each damping coefficient) for comparison. Please use the subplot command.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:1
Free Vibration Response of Single Degree of
Freedom System(100 %)
Figure 1 represent a simple vibration system.
The free vibration response of an undamped single degree of freedom (SDOF)
oscillator is given by its displacement x(t) satisfying
x(t) = x(0)sin*(wt)e-2dwt + v(0)
(1)
-cos(wt)e-10dwt
%3D
where t is time in seconds and w = Vis the natural frequency of the system
with m and k being the mass and the stiffness of the system. d is the damping
coefficient of the system. Define v(t) and a(t) as the time dependent velocity and
acceleration of the system.
Write an M-file script using functions that will compute and plot
1. The displacement of the system x(t) over time
2. The velocity of the system v(t) over time
3. The acceleration of the system a(t) over time
for three damping coefficients (d = 0,1,5) within a time interval 0 < t < 10
s. You will need THREE(3) functions, one for each displacement, velocity and
acceleration calculations. Assume m = 10, k = 1 and that r(0) = v(0) = 10.
Note that x(t), v(t), a(t) should be on ONE plot for each damping coefficient.
Use the a solid line for the displacement, broken-lines for the velocity and dotted
lines for acceleration. Thus, your code needs to produce THREE plots (one for
each damping coefficient) for comparison. Please use the subplot command.
Transcribed Image Text:Note that x(t), v(t), a(t) should be on ONE plot for each damping coefficient.
Use the a solid line for the displacement, broken-lines for the velocity and dotted
lines for acceleration. Thus, your code needs to produce THREE plots (one for
each damping coefficient) for comparison. Please use the subplot command.
To ensure that your plot will be reasonably smooth, choose a time increment
in your displacement and velocity calculations that is no larger than 1/10th of
the system period T = 21I /m/k.
x(t)
Fig. 1: Vibration of the System.
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