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(a) Suppose two identical pendulums are coupled by means

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill ISBN: 9781111827052 44

Solution for problem 47RP Chapter 7.R

A First Course in Differential Equations with Modeling Applications | 10th Edition

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A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 47RP

Problem 47RP

(a) Suppose two identical pendulums are coupled by means of a spring with constant k. See Figure 7.R.11. Under the same assumptions made in the discussion preceding Example 3 in Section 7.6, it can be shown that when the displacement angles u1(t) and u2(t) are small, the system of linear differential equations describing the motion is

Use the Laplace transform to solve the system when where constants. For convenience let ω2 = g/l, K = k/m.

(b) Use the solution in part (a) to discuss the motion of the coupled pendulums in the special case when the initial conditions are θ1(0) = θ0,   When the initial conditions are

Step-by-Step Solution:
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Spinal Nerves and Reflexes Lower Extremity Nerves ● Femoral Nerve ○ Innervation= muscles of anterior thigh ○ Action= flex hip and extend knee ○ Skin Connection= anterior thigh and medial leg ● Obturator Nerve ○ Innervation= muscles of medial thigh ○ Action= adduction ○ Skin Connection= upper and inner thigh ● Tibial Nerve *part of sciatic nerve ○ Innervation= muscles of the posterior thigh and leg ○ Action= knee, plantar and toe flexion, hamstrings (hip flexion, knee flexion) ○ Skin Connection: bottom of foot

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Chapter 7.R, Problem 47RP is Solved
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Textbook: A First Course in Differential Equations with Modeling Applications
Edition: 10
Author: Dennis G. Zill
ISBN: 9781111827052

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(a) Suppose two identical pendulums are coupled by means