- #1
Salvador_
- 18
- 2
Homework Statement
A particle of mass m is subject to a force F (x) = -kx. The initial position is
zero, and the initial speed is v0. Find x(t).
Homework Equations
F = m*v*dv/dx = -kx
v = dx/dt
The Attempt at a Solution
I'm new to differential equations, so please excuse me if I make any amateurish mistakes.
-kx = mv*dv/dx
After integrating:
-kx2/2 + c = mv2/2
v2 = -kx2 + c
This is the part I'm unsure about, the inital values:
v2(0) = 0 + c = v02
So c = v02
v = (v02 - kx2/m)1/2
dx/v(x) = dt
After integrating: (a bit messy)
t = (m/k)1/2*arcsin(x*(k/v02m)1/2) + c
c=0
Just wanted to know if I went wrong somewhere as I'm not convinced by the final answer.