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Problem:

 

In a spring test, Eddie releases the spring from rest at a height of 20 cm beyond the spring's natural length (i.e. y(0)=20). He finds that the resulting vibration has a period of 1 s and that the amplitude of the vibration halves after 3 s ("half-life"). From his knowledge of damped springs, he also knows that the spring should behave according to the equation y(t)=Aebtcos(ct)

 

Question:

Solve the function paramaters A, b and c

 

I've solved A = 20 by setting time = 0

And as the period = 1s then C must = 2pi (at least I believe)

 

just having trouble finding B. I know I have to set the function to half (y(t)/2) however that still leaves me with an unknown answer and an unknown variable.

 

Any help is much appreciated!

 Mar 5, 2018
 #1
avatar+2234 
+3

Solution:

 

Period =2πc=1,so c=2πThen x=20e(bt)cos(2πt)When t = 3, then x = 1010=20e(3b)cos(6π)0.5=e(3b)1Ln(0.5)=(3b)3b=Ln(0.5)3b=0.69314718b=0.23104906018 20e(0.231049060183)cos(6π3)=10 (check)a=20,b=0.23104906018,c=2π

 

Edit: Cosmetic

GA

 Mar 5, 2018
edited by GingerAle  Mar 6, 2018
 #2
avatar+251 
+1

Thank you!

 

Ended up getting there in the end, but wanted to keep the question up so I could get my answer confirmed.

 

Thanks for your help.

 Mar 6, 2018

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