Q1 Problem 1: Assume that two variable forces F₁ and F2 are being applied to the following massesm₁ and m2, respectively. Derive the system of differential equations describing the straight-linehorizontal motion of the coupled springs shown in equilibrium shown in the figure. Solve thesystem when k₁ = 1, k2 = 1, k3 = 1, m₁ = 1, m2 = 1, C₁ = 0, C2 = 0, C3 = 0 and x₁ (0) = 0, x'ı (0) = -1,X2(0)=0, x'2(O) = 1. (Note: Assume that the system vibrates free without any periodic driven load,F₁-F₂=0)x₁ (1)x₂ (1)C₁m₁F₁(t)k₂wwwC₂m₂> F₂(1)k₂wwwC₁

k1=1k2=1k3=1m1=1m2=1c1=0c2=0c3=0x10=0x1'0=-1x20=0x2'0=1Assume F1=F2=0 To-Find:- Differential…

Engineering

Mechanical Engineering

1

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

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

Problem 1: Assume that two variable forces F₁ and F2 are being applied to the following masses
m₁ and m2, respectively. Derive the system of differential equations describing the straight-line
horizontal motion of the coupled springs shown in equilibrium shown in the figure. Solve the
system when k₁ = 1, k2 = 1, k3 = 1, m₁ = 1, m2 = 1, C₁ = 0, C2 = 0, C3 = 0 and x₁ (0) = 0, x'ı (0) = -1,
X2(0)=0, x'2(O) = 1. (Note: Assume that the system vibrates free without any periodic driven load,
F₁-F₂=0)
x₁ (1)
x₂ (1)
C₁
m₁
F₁(t)
k₂
www
C₂
m₂
> F₂(1)
k₂
www
C₁

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