# Derivation of equation of motion from various forces.

1. Feb 21, 2009

### Holychikenz

1. The problem statement, all variables and given/known data

A particle of mass m is acted on by the forces as given below. Solve these equations
to find the motion of the particle in each case.

(a) F(x, t) = k(x + t2), with x = x0 and v = v0 = 0 when t = 0;
(b) F(x', t) = kx^2 x', with x = x0 and v = v0 = 0 when t = 0;
(c) F(x', t) = k(ax'+ t), with v = v0 when t = 0;
(d) F(x, x') = ax^2/x';
(e) F(x, x', t) = k(x + x't).

(a) I didn't have any trouble with as it was just a simple non homogeneous 2nd order ODE. The others to me seemed nonlinear and very difficult for some reason. I'm wondering how the variables which F is dependent on might affect the problems and if there is some method for solving these kinds of ODE's. Also my professor said that for each one to solve for x(t).

2. Feb 21, 2009

### Holychikenz

In part (b) I get as far as solving for v(t), but to solve for x(t) I'm left with the integral of (1/(x^3 + x0^3)). Is very messy and ends up being tan-1(some function of x) + ln(another function of x). Because of that I can't solve for just x in terms of only t.

3. Feb 21, 2009

### gabbagabbahey

For part (b), what is F(t=0)?....If the force on the particle is proportional to the speed, and its initial speed is zero, will the particle ever actually go anywhere?