Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 17 - Second-Order Differential Equations - 17.3 Applications of Second-Order Differential Equations - 17.3 Exercises: 1

Answer

$x(t)=0.35cos(2\sqrt{5}+1)$

Work Step by Step

$k(0.25)=25$ $k=100$ $5r^2+100=0$ $r=2\sqrt{5}$ $x(t)=c_{1}cos(2\sqrt{5}t)+c_{2}sin(2\sqrt{5})$ $x(0)=0.35$ $c_{1}=0.35$ $x'(t)=-2\sqrt{5}(0.35)sin(2\sqrt{5}t)+2\sqrt{5}c_{2}cos(2\sqrt{5}t)$ $x'(0)=0$ $c_{2}=0$ $x(t)=0.35cos(2\sqrt{5}+1)$
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