(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

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

(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

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