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Unformatted text preview: quation for
the second equation results in , we obtain . Substitution into Rearranging the terms, the single differential equation for is .
The general solution is
With given in terms of , it follows that
. Imposing the specified initial conditions, we obtain and . Hence and 13. Solving the first equation for
the second equation results in , we obtain . . Substitution into ________________________________________________________________________
page 338 —————————————————————————— CHAPTER 7. —— Rearranging the terms, the single differential equation for is
. 15. Direct substitution results in Expanding the left-hand-side of the first equation, Repeat with the second equation to show that the system of ODEs is identically satisfied.
16. Based on the hypothesis, Subtracting the two equations, Similarly, Hence the difference of the two solutions satisfies the homogeneous ODE.
17. For rectilinear motion in one dimension, Newton's second law can be stated as The
force exerted by a linear spring is given by...
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- Spring '08