The vertical motion of a mass attached to a spring is described by t.pdf

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lejeunehayneswowel96

The vertical motion of a mass attached to a spring is described by the IVP Solution the associated equation is 1/4x^2+x+1=0 or x^2+4x+4=0 (x+2)^2=0 so the solution is of the form x=Ae^(-2t)+Bte^(-2t) using x(0)=4 we get A=4 x\'(0)=-2A+B=2 B=10 x=4e^(- 2t)+10te^(-2t) x\'=-8e^(-2t)+10e^(-2t)-16te^(-2t)=0 2-16t=0 t=1/8 x\'>0 before 1/8 and x\'>0 after 1/8 So the maximum vertical is when t=1/8.

The vertical motion of a mass attached to a spring is described by the IVP
Solution
the associated equation is 1/4x^2+x+1=0 or x^2+4x+4=0 (x+2)^2=0 so the solution
is of the form x=Ae^(-2t)+Bte^(-2t) using x(0)=4 we get A=4 x'(0)=-2A+B=2 B=10 x=4e^(-
2t)+10te^(-2t) x'=-8e^(-2t)+10e^(-2t)-16te^(-2t)=0 2-16t=0 t=1/8 x'>0 before 1/8 and x'>0
after 1/8 So the maximum vertical is when t=1/8

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