I am looking for a confirmation on starting my Problem...
We have a Driven Simple Harmonic Oscillator that is undamped.
Initial Conditions are x[0]=0 and v[0]=0..

For my Homogeneous Solution:
I have my initial of x = A cos(wt+p)
Where I used x[0] and got p = pi/2

Should I switch over my initial guess to a A sin(wt) instead and then work onto the Non-Homogeneous and get my total solution by:
x_tot = x_trans + x_ss
= A sin(wt) + ?

I have a forced motion denoted with the function F_0 sin(wt)

Question

I am looking for a confirmation on starting my Problem...
We have a Driven Simple Harmonic Oscillator that is undamped.
Initial Conditions are x[0]=0 and v[0]=0..

For my Homogeneous Solution:
I have my initial of x = A cos(wt+p)
Where I used x[0] and got p = pi/2

Should I switch over my initial guess to a A sin(wt) instead and then work onto the Non-Homogeneous and get my total solution by:
x_tot = x_trans + x_ss
= A sin(wt) + ?

I have a forced motion denoted with the function F_0 sin(wt)

mani_jha · Answer

Yeah, it will be simpler to use a sine function as initial, because there will be no phase difference that you have to take into account then.

anonymous · Answer

Thanks, tried it that way but 2 hours later I erased everything and realized that I can rock it using the C1 cos(wt) + C2 sin(wt) solution was much more versitile..