write the second order diff eq for an RLC circuit set it equal to a forcing function, the output will be the convolution of the RLC impulse response with the forcing function, I am looking at oscillators that have an infinite number of modes available to them, perhaps I am using the wrong...
something like an electrical oscillator..let me refine my question a little better. If I drive my electrical oscillator at a certain frequency continuously, my feeling is the output would reflect only that frequency and none of the harmonics. On the other hand, if I drove the oscillator at a...
If I have a oscillator that has an infinite number of harmonics, what decides which harmonics are excited? Is it whatever frequency inputs I drive into the system, and the system damps out frequencies that don't match the harmonics or is it possible that driving at only one harmonic frequency...
I know that as water waves get closer to shore, amplitude increases via energy conservation, and from what I have read shallow water behaves analogously to an increasingly dense medium (or at least higher index of refraction). If I try and extend this analogy to sound wave/wave on...
Homework Statement
find the arc length
x=2e^t, y=e^-t, z=2t
Homework Equations
The Attempt at a Solution
dr/dt=2e^ti-e^-tj+2
ds/dt=sqrt((4e^2t)+(e^-2t)+4)) dt
=integral from 0 to 1 sqrt(4e^4t+4e^2t+1)/e^t
sorry about the lack of latex, I have no idea how to integrate this function
Homework Statement
Prove that the line of intersection of the planes x+2y-z=2 and 3x+2y+2z=7 is parallel to the line x=1+6t, y=3-5t, z=2-4t. find an equation of the plane determined by the two lines
[b]3. The Attempt at a Solution [/
cross product of n1 by n2 to determine direction of...
Homework Statement
suppose x=x0+tv and y=y0+sw are two parametric representations of the same line l in r^n
a. show that there are scalars t0 and s0 such that y0=x0+t0v and x0=y0+s0w
b. show that v and w are parallel
The Attempt at a Solution
a. same line thus
y0+sw=x0+tv
when...