Q2 A mass-spring system is shown in Figure Q2 with mi = 10 kg, m2 = 20 kg, kı = (10+P) N/m, k2 = (10+Q) N/m and k3 = (20+R) N/m. (a) If the system is made to vibrate freely in vertical direction, draw a free body diagram for the system. (b) Proof that the equation of motion for the system as: - k, T (k, +k,)]|x2, D-8 m, + 0 m2 -k, (c) Determine the natural frequencies of the system. (d) Evaluate and illustrate the mode shapes of the system. Note Q2: The values of P, Q and R depend on the respective 4th, 5th, and 6th digit of your matric number as the following number format AD XXXPQR. For example, if your matric number is AD 170154 gives the value P = 1, Q = 5 and R = 4, thus %3D the spring stiffness, ki = 11 N/m, k2 = 15 N/m, and k3 = 24 N/m
Q2 A mass-spring system is shown in Figure Q2 with mi = 10 kg, m2 = 20 kg, kı = (10+P) N/m, k2 = (10+Q) N/m and k3 = (20+R) N/m. (a) If the system is made to vibrate freely in vertical direction, draw a free body diagram for the system. (b) Proof that the equation of motion for the system as: - k, T (k, +k,)]|x2, D-8 m, + 0 m2 -k, (c) Determine the natural frequencies of the system. (d) Evaluate and illustrate the mode shapes of the system. Note Q2: The values of P, Q and R depend on the respective 4th, 5th, and 6th digit of your matric number as the following number format AD XXXPQR. For example, if your matric number is AD 170154 gives the value P = 1, Q = 5 and R = 4, thus %3D the spring stiffness, ki = 11 N/m, k2 = 15 N/m, and k3 = 24 N/m
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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Question
pls ans quickly
take p= 2 q=0 r=1
Transcribed Image Text:kz
m2
x2(t)
Figure Q2
00000
Transcribed Image Text:Q2
A mass-spring system is shown in Figure Q2 with mı =
10 kg, m2 = 20 kg, k= (10+P)
N/m, k2 = (10+Q) N/m and k3 = (20+R) N/m.
(a) If the system is made to vibrate freely in vertical direction, draw a free body diagram
for the system.
(b) Proof that the equation of motion for the system as:
(k, + k,)
-k,
(k, + kz
m,
m2 |[ä,
-k,
(c) Determine the natural frequencies of the system.
(d) Evaluate and illustrate the mode shapes of the system.
Note Q2: The values of P, Q and R depend on the respective 4th, 5th, and 6th digit
of your matric number as the following number format AD XXXPQR. For example,
if your matric number is AD 170154 gives the value P = 1, Q = 5 and R = 4, thus
the spring stiffness, ki = 11 N/m, k2 = 15 N/m, and k3 = 24 N/m
%3D
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