Explore BrainMass

LaPlace Transformations with some Initial Value Problems

Problem 9.1 (Prob. 29. P. 252) Two particles each of mass m moves in the plane with co-ordinates (x(t), y(t)) under the influence of a force that is directed toward the origin and had magnitude k/(x2 + y2) an inverse-square central force field. Show that mx''=-kx/(r^3) and my''= -ky/(r^3) where r = sqrt(x2 + y2)

Problem 9.2 (Prob. 30, P. 252) suppose that a projectile of mass in moves in a vertical plane in the atmosphere near the surface of the earth under the influence of two forces: a downward gravitational force of magnitude mg and a resistive force FR that is directed opposite to the velocity vector v and has magnitude kv^2 (where v = |v| is the speed of the projectile). Show that the equations of motion of the projectile are
mx" = ?kvx'
my" =?kvy"?mg

Problem 9.3 Use Laplace Transfonn to find the particular solutions of the following systems
x' = ?y
x(0) = 0
y(0) = 3

Please see attached for the rest of this question, and all other questions.


Solution Preview

Hello and thank you for posting your question to Brainmass!
The solution is attached below in two Word XP ...

Solution Summary

Eight problems involving Laplace Transformations and Initial-Value Problems are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.