Hi,
I'm trying to solve for the steady-state current i through an RL network as a result of a non-sinusoidal voltage.
(di/dt) + (R/L)i = v(t)
where v(t) is a "shark's fin" wave: V*sin(t) for 0 <= t < pi/2 and then repeat.
I could do this by finding the fourier series for v(t), and then solving the dif-eq for each of the fourier terms.
I'm wondering if there is another, more direct way? Is there any way to take advantage of the fact that my input function is, in fact, a sinusoidal function, just a portion of it instead of the whole thing?
Finally, what is the mathematically proper way to write v(t)? Is it:
v(t) = V*sin(t) {0 <= t < pi/2} or
v(t) = V*sin(t) {0 <= t < T} where T = pi/2 = Period
or something else? How does the statement of v(t) imply that the period from 0 to pi/2 continues and repeats, instead of v(t) being valid only up to time pi/2 and then the function stops?
Thanks.
I'm trying to solve for the steady-state current i through an RL network as a result of a non-sinusoidal voltage.
(di/dt) + (R/L)i = v(t)
where v(t) is a "shark's fin" wave: V*sin(t) for 0 <= t < pi/2 and then repeat.
I could do this by finding the fourier series for v(t), and then solving the dif-eq for each of the fourier terms.
I'm wondering if there is another, more direct way? Is there any way to take advantage of the fact that my input function is, in fact, a sinusoidal function, just a portion of it instead of the whole thing?
Finally, what is the mathematically proper way to write v(t)? Is it:
v(t) = V*sin(t) {0 <= t < pi/2} or
v(t) = V*sin(t) {0 <= t < T} where T = pi/2 = Period
or something else? How does the statement of v(t) imply that the period from 0 to pi/2 continues and repeats, instead of v(t) being valid only up to time pi/2 and then the function stops?
Thanks.