Find x(t) with Kx Force and Mass m | KxForce

[Ryan95]

Homework Statement

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).

Homework Equations

F(x)=kx
F=ma

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).

 

[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.