# Math Help - Mass-Spring System Beats and Resonance

1. ## Mass-Spring System Beats and Resonance

In the Beat not have friction force, correct ?

$m \frac{d^2x}{dt^2} + kx = F_o cos(wt)$

We can write as

$\frac{d^2x}{dt^2} + w_o^2 x = \frac{F_o}{m} cos(wt)$

If $w \not= w_o$

Assuming (Particular solution)
$x_p = acos(wt) + bsin(wt)$
Why we have assuming this ?

How find $a(w_o^2 - w^2)cos(wt) + b(w_o^2 - w^2)sin(wt) = \frac{F_o}{m} cos(wt)$ ???

And why find that $x_p = \frac{F_o}{m(w_o^2 -w^2)}cos(wt)$ ??

2. In the equation

$\frac{d^2x}{dt^2} + w_o^2 x = \frac{F_o}{m} cos(wt)$

$w_o$ is the frequency of oscillation of the system and $w$ is frequency of oscillation of the external force ???