(a) Explanation It is given that, s ( t ) = e − f t 2 m ( A . sin ( 4 k m − f 2 2 m t ) + B . cos ( 4 k m − f 2 2 m t ) ) Differentiating above equation with respect to ‘t’ s ' ( t ) = e − f t 2 m ( A . sin ( 4 k m − f 2 2 m t ) + B . cos ( 4 k m − f 2 2 m t ) ) . − f 2 m + e − f t 2 m ( A . cos ( 4 k m − f 2 2 m t ) − B . sin ( 4 k m − f 2 2 m t ) ) . 4 k m − f 2 2 m s ' ( t ) = ( s ( t ) ) . − f 2 m + e − f t 2 m ( A . cos ( 4 k m − f 2 2 m t ) − B . sin ( 4 k m − f 2 2 m t ) ) . 4 k m − f 2 2 m − − − − − − − − ( 1 ) Now, e − f t 2 m ( A . cos ( 4 k m − f 2 2 m t ) − B . sin ( 4 k m − f 2 2 m t ) ) . 4 k m − f 2 2 m = s ' ( t ) + ( s ( t ) ) . f 2 m -----(2) Now, differentiating (1) with respect to ‘t’ s ' ' ( t ) = − f 2 m . s ' ( t ) + e − f t 2 m ( A (b) To determine The proof that A = 2 m v 0 + f s 0 4 k m − f 2 and B=s 0 with an initial position of s 0 and initial velocity of v 0

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Question

Chapter 2.6, Problem 79A

(a)

To determine

The proof that the function s(t) has the property that s''(t)+fms'(t)+kms(t)=0

(b)

To determine

The proof that A=2mv0+fs04km−f2 and B=s0 with an initial position of s0 and initial velocity of v0

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Chapter 2.6, Problem 78A

Chapter 2.6, Problem 80A

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Chapter 2 Solutions

Calculus Combo

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The proof that the function s ( t ) has the property that s ' ' ( t ) + f m s ' ( t ) + k m s ( t ) = 0

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The proof that the function s(t) has the property that s''(t)+fms'(t)+kms(t)=0

The proof that A=2mv0+fs04km−f2 and B=s0 with an initial position of s0 and initial velocity of v0

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Chapter 2 Solutions