# Kx force, find x(t)

#### Ryan95

1. The problem statement, all variables and given/known data
A particle of mass m is subject to force F(x)=kx with K>0. The initial starting position is x0 and the initial speed is zero. Find x(t).

2. Relevant equations
F(x)=kx
F=ma

3. The attempt at a solution
Honestly, I am totally lost on this. I've written acceleration as v(dv/dx) which gave me mv(dv/dx)=Kx and then tried separating variables to integrate, but once I do that, I'm totally lost as I end up with m(v2/2)=K(x2/2).

Last edited:
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#### drvrm

Honestly, I am totally lost on this. I've written acceleration as v(dv/dt) which gave me mv(dv/dx)=Kx and then tried separating variables to integrate, but once I do that, I'm totally lost as I end up with m(v2/2)=K(x2/2).
i wonder how one can write acceleration as v..dv/dt as we know it as rate of change of velocity with time.. may be a typo.
now dv/dt can be expressed as d/dxof v multiplied by dx/dt .

i think you should proceed with the analysis as per the rule of integration and have initial conditions at t=0 and try to find x as a function of t. as one normally does with constant forces.

#### Ryan95

i wonder how one can write acceleration as v..dv/dt as we know it as rate of change of velocity with time.. may be a typo.
now dv/dt can be expressed as d/dxof v multiplied by dx/dt .

i think you should proceed with the analysis as per the rule of integration and have initial conditions at t=0 and try to find x as a function of t. as one normally does with constant forces.
Oh, thank you, yes that was a typo. I've edited the post.

"Kx force, find x(t)"

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