Explanation Given information: Let x ( t ) be the angle the pendulum makes with the vertical (measured in radians). d 2 x d t 2 = − 8 L x , where g is the acceleration due to gravity ( g ≈ 9.81 m/s 2 ) . Calculation: We will first the characteristic equation for the given DE: λ 2 + g L = 0 λ = ± i g L So the solution is of the following form: x ( t ) = cos [ t g L ] + sin [ t g L ] Since the extreme positions the velocity is zero, we will find Δ t such that x ' ( t ) = 0 then x ' ( Δ t ) = 0 . Equal the following with zero and get x ' ( t ) = − g L sin [ t g L ] + g L cos [ t g L ] = 0 Hence we get g L cos t

Linear Algebra with Applications (2-Download)

5th Edition

ISBN: 9780321796974

Author: Otto Bretscher

Publisher: PEARSON

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Chapter 9.3, Problem 33E

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To find: time taken by pendulum have to be so that it swings from one extreme position to the other in exactly one second.

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Chapter 9.3, Problem 32E

Chapter 9.3, Problem 34E

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Chapter 9 Solutions

Linear Algebra with Applications (2-Download)

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time taken by pendulum have to be so that it swings from one extreme position to the other in exactly one second.

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Chapter 9 Solutions