A two-mass system consists of a piston of mass m₁, connected by two elastic springs, that moves inside a tube as shown in Fig. 5.23. A pendulum of length / and end mass m₂ is con- nected to the piston as shown in Fig. 5.23. (a) Derive the equations of motion of the system in terms of x₁(1) and 0(1). (b) Derive the equations of motion of the system in terms of the x₁ (1) and x₂(1). (c) Find the natural frequencies of vibration of the system.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Please just question C. Instead of solving part C how it says can you solve by using k1=k2=1N/m m1=m2=1kg, l=1m, g=10m/s^2, use [X,wn2]=eig(K,M) to find the natural frequencies for both sets of coordinates. Thank you
000000
M₁
0(1)
k₂
xxxxxxxxx0000
-12-|
FIGURE 5.23 Piston-pendulum motions.
Transcribed Image Text:000000 M₁ 0(1) k₂ xxxxxxxxx0000 -12-| FIGURE 5.23 Piston-pendulum motions.
5.4 A two-mass system consists of a piston of mass m₁, connected by two elastic springs, that
moves inside a tube as shown in Fig. 5.23. A pendulum of length / and end mass m₂ is con-
nected to the piston as shown in Fig. 5.23. (a) Derive the equations of motion of the system
in terms of x₁ (1) and 0(1). (b) Derive the equations of motion of the system in terms of the
x₁ (1) and x₂(1). (c) Find the natural frequencies of vibration of the system.
Transcribed Image Text:5.4 A two-mass system consists of a piston of mass m₁, connected by two elastic springs, that moves inside a tube as shown in Fig. 5.23. A pendulum of length / and end mass m₂ is con- nected to the piston as shown in Fig. 5.23. (a) Derive the equations of motion of the system in terms of x₁ (1) and 0(1). (b) Derive the equations of motion of the system in terms of the x₁ (1) and x₂(1). (c) Find the natural frequencies of vibration of the system.
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