(1) A rigid bar (OA)with mass m and length L is simply supported at one end and free at the other end .A lumped mass M fixed at the end of A is subjected to a vertical harmonic excitation f(t). Two springs (k) are connected at the length a and b of the bar. Please calculate the natural frequency and response vibration of the system. (Figure 1) Note: m=10kg, L=1 m, a=0.25m, b=0.5m, k-5000N/m, M=50kg, f(t)=FcosQt (F=500N, Q=1000rpm). The vibration is very small. a b k L MA k m M Figure 1: Single Degree Vibration System f(t) A
(1) A rigid bar (OA)with mass m and length L is simply supported at one end and free at the other end .A lumped mass M fixed at the end of A is subjected to a vertical harmonic excitation f(t). Two springs (k) are connected at the length a and b of the bar. Please calculate the natural frequency and response vibration of the system. (Figure 1) Note: m=10kg, L=1 m, a=0.25m, b=0.5m, k-5000N/m, M=50kg, f(t)=FcosQt (F=500N, Q=1000rpm). The vibration is very small. a b k L MA k m M Figure 1: Single Degree Vibration System f(t) A
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Problem 1.1MA
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![(1) A rigid bar (OA)with mass m and length L is simply supported at
one end and free at the other end .A lumped mass M fixed at the
end of A is subjected to a vertical harmonic excitation f(t). Two
springs (k) are connected at the length a and b of the bar. Please
calculate the natural frequency and response vibration of the
system. (Figure 1)
Note: m=10kg, L=1 m, a=0.25m, b=0.5m, k-5000N/m, M=50kg,
f(t)=Fcos.Qt (F=500N, Q=1000rpm). The vibration is very small.
a
b
k
L
k
+
m
M
Figure 1: Single Degree Vibration System+
f(1)
A
X
(2) Please write out the Equation of Movements of the following system
using matrix. (Figure 2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05ed4213-5832-4388-9cf2-f1d506899ead%2F832b6b46-afe7-4173-9236-013c815b2638%2Fdw5abs9i_processed.png&w=3840&q=75)
Transcribed Image Text:(1) A rigid bar (OA)with mass m and length L is simply supported at
one end and free at the other end .A lumped mass M fixed at the
end of A is subjected to a vertical harmonic excitation f(t). Two
springs (k) are connected at the length a and b of the bar. Please
calculate the natural frequency and response vibration of the
system. (Figure 1)
Note: m=10kg, L=1 m, a=0.25m, b=0.5m, k-5000N/m, M=50kg,
f(t)=Fcos.Qt (F=500N, Q=1000rpm). The vibration is very small.
a
b
k
L
k
+
m
M
Figure 1: Single Degree Vibration System+
f(1)
A
X
(2) Please write out the Equation of Movements of the following system
using matrix. (Figure 2)
![Note: Lagrange's approach is recommended.
P₂(t)
k₁
k5
www
P₁(t)
k₂ m₂
wwwm,ww
m₁
k3
k6
www
P3(t)
k₁
wwwm3wWw
Figure 2: N Degree Vibration System](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05ed4213-5832-4388-9cf2-f1d506899ead%2F832b6b46-afe7-4173-9236-013c815b2638%2F4azr5ihj_processed.png&w=3840&q=75)
Transcribed Image Text:Note: Lagrange's approach is recommended.
P₂(t)
k₁
k5
www
P₁(t)
k₂ m₂
wwwm,ww
m₁
k3
k6
www
P3(t)
k₁
wwwm3wWw
Figure 2: N Degree Vibration System
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