(adsbygoogle = window.adsbygoogle || []).push({}); 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).

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# Derivation of equation of motion from various forces.

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