For the mass spring damper system shown in the figure, assume that m = 0.25 kg, k= 2500 N/m, and c = 10 N.s/m. The values of force measured at 0.05-second intervals in one cycle are given below. 0.10 14 0.15 44 0.20 19 0.25 33 0.30 34 time 0.05 0.35 0.40 F(t) 12 12 22 time 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 Force 32 11 18 25 30 49 40 35 21 time 0.90 0.95 F(t) 11 +x F(t) 1- Find the equation of motion. 2- Find the homogenous solution. 3- If we excite the system with initial displacement and velocity as 5 mm and 0.2 m/s respectively, plot the response of the free vibration system.
For the mass spring damper system shown in the figure, assume that m = 0.25 kg, k= 2500 N/m, and c = 10 N.s/m. The values of force measured at 0.05-second intervals in one cycle are given below. 0.10 14 0.15 44 0.20 19 0.25 33 0.30 34 time 0.05 0.35 0.40 F(t) 12 12 22 time 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 Force 32 11 18 25 30 49 40 35 21 time 0.90 0.95 F(t) 11 +x F(t) 1- Find the equation of motion. 2- Find the homogenous solution. 3- If we excite the system with initial displacement and velocity as 5 mm and 0.2 m/s respectively, plot the response of the free vibration system.
Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
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![Your project must be typed with cover page (no handwritten projects will be accepted)
For the mass spring damper system shown in the figure, assume that m = 0.25 kg, k= 2500 N/m,
and c = 10 N.s/m. The values of force measured at 0.05-second intervals in one cycle are given
below.
time
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
F(t)
12
14
44
19
33
34
12
22
time
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
Force
32
11
18
25
30
49
40
35
21
time
0.90
0.95
F(t)
11
k
m
+x
F(t)
1- Find the equation of motion.
2- Find the homogenous solution.
3- If we excite the system with initial displacement and velocity as 5 mm and 0.2 m/s
respectively, plot the response of the free vibration system.
4- Use the generated plot in part 3 to verify the value of the damping constant, c.
5- Find the steady state solution (only particular solution) for the forced vibration system.
Take number of terms in your Fourier series terms from this range [ 30 – 55].
6- Plot the force in the table, and the Fourier series expansion of the force (same graph).
7- Plot the steady state solution.
8- Find the total solution for the forced system with the initial conditions given in part 3.
9- Plot the total solution found in part 8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56a72e11-b103-4489-abab-5a781cca5d51%2F64ce43c5-294e-4c0a-9f4e-018e07ba3c3b%2Fmdeyzo_processed.gif&w=3840&q=75)
Transcribed Image Text:Your project must be typed with cover page (no handwritten projects will be accepted)
For the mass spring damper system shown in the figure, assume that m = 0.25 kg, k= 2500 N/m,
and c = 10 N.s/m. The values of force measured at 0.05-second intervals in one cycle are given
below.
time
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
F(t)
12
14
44
19
33
34
12
22
time
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
Force
32
11
18
25
30
49
40
35
21
time
0.90
0.95
F(t)
11
k
m
+x
F(t)
1- Find the equation of motion.
2- Find the homogenous solution.
3- If we excite the system with initial displacement and velocity as 5 mm and 0.2 m/s
respectively, plot the response of the free vibration system.
4- Use the generated plot in part 3 to verify the value of the damping constant, c.
5- Find the steady state solution (only particular solution) for the forced vibration system.
Take number of terms in your Fourier series terms from this range [ 30 – 55].
6- Plot the force in the table, and the Fourier series expansion of the force (same graph).
7- Plot the steady state solution.
8- Find the total solution for the forced system with the initial conditions given in part 3.
9- Plot the total solution found in part 8.
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