Simple ODE, I don't know what I'm doing wrong

[HmBe]

Homework Statement

solve x''(t)+w²x(t)=-gsin(a) with x(0)'=0 x(0)=-gsin(a)/w²

Homework Equations

The Attempt at a Solution

let x=Acoswt+Bsinwt+C
x'=0 so B=0

x=Acoswt+C
c=-gsina/w²

t=0, x=A-gsina/w²
but x(0)=-gsin(a)/w²

so A=0, and you get x is a constant, which makes no sense for the situation.

 

[Char. Limit]

It may make no sense, but it does work. I checked it, and your solution matches the conditions for the differential equation.

 

[LCKurtz]

Homework Statement

solve x''(t)+w²x(t)=-gsin(a) with x(0)'=0 x(0)=-gsin(a)/w²

Homework Equations

The Attempt at a Solution

let x=Acoswt+Bsinwt+C
x'=0 so B=0

x=Acoswt+C
c=-gsina/w²

t=0, x=A-gsina/w²
but x(0)=-gsin(a)/w²

so A=0, and you get x is a constant, which makes no sense for the situation.

You need to get the general solution of the non-homogeneous equation before you plug in the initial conditions to evaluate the constants. You have the general solution of the homogeneous equation:

x_c = A cos(wt) + B sin(wt)

The next step is to find a particular solution x_p of the non-homogeneous equation. So figure out what C will give

x_p = C

as a solution of the NH equation. This has nothing to do with the initial conditions. Once you have C figured out your general solution is

x_c = A cos(wt) + B sin(wt) + C

Only then should you plug in the initial conditions for x(0) and x'(0) to figure out A and B.