0:00
Question.
00:01
You're giving a damper.
00:03
Basically is a damped harmonic oscillator with mass m.
00:10
And obviously the equation motion for this damp time oscillator is m times acceleration equals the force.
00:20
And you have three forces.
00:22
One is they recall your first, which is simply minus k times x.
00:26
K is brain constant.
00:28
And you have the first, uh, the damping first, which is minus b, b is the dammit coefficient times the velocity, x.
00:37
Dot.
00:37
And of course, you also have the first external force, which is i'll write as f, um, n, sine, omega, t.
00:53
So, um, all you can rewrite this equation as, you can realize this equation as, um, x dot divided by m on both sides, plus k over m x plus b over m x.
01:15
Dot equals f0 sine omega t.
01:24
Now the solution to this equation has two parts.
01:35
The first part, i'll write the solution as xt.
01:39
The first part is the part that solves the homogeneous part of this equation.
01:45
And that part, you can always write that homogeneous part, you can always write as a to the power of b over 2m times t...