- #1
thename1000
- 18
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Homework Statement
Trying to go over this part of my test review. I'm not understanding how to do this. The specific problem which I actually have worked out in my notes:
A diff equation model of the motion of a spring where x is displacement from the spring's natural length, k is the spring constant, and m is the mass as follows:
(d^2*x)/(d*t^2) = k/m * x
Show that x(t)=sin(sqrt(k/m)*t) + 2cos(sqrt(k/m)*t) is a solution to the model.
The Attempt at a Solution
My notes appear to take the first, then the second dir. of the second function there. But that's all I can make sense of. Maybe I'm not understanding how to take the dir of these functions I'm not sure.
For example on the second to the last line, how am I supposed to simplify -k/m (sin(sqrt(k/m)t) + 2cos (sqrt(k/m)t)
to
-k/mx
thanks for any help!