Chapter 17 - Second-Order Differential Equations - 17.3 Applications of Second-Order Differential Equations - 17.3 Exercises - Page 1215: 1

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

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