7

[TOP LEFT NOTES:]

(dμ[^]→[/^])/(dt) = Ɣ (μ[^]→[/^] x H[^]→[/^])

H[v]x[/v] = H[v]1[/v] cos ωt

H[v]y[/v] = ŦH[v]1[/v] sin ωt

(D/(dt)) (μ[^]→[/^])' = Ɣ {(μ[^]→[/^])' x (-((ω[^]→[/^])/(|Ɣ|))+((H[^]→[/^])'))}
= Ŧ{({left tailed ω}[^]→[/^]) (((t)(ω[^]→[/^])) ¤ (|Ɣ|)(H'))}

(μ[^]→[/^])' precesses about the fixed vector

(H[^]→[/^])' - (((ω[^]→[/^]))/(|Ɣ|)) with an angular velocity

{backwards ʎ} = square root of {(-ω + |Ɣ| H[v]0[/v])[^]2[/^] + (Ɣ[^]2[/^]H[v]1[/v][^]2[/^])} = square root of {(ω[v]0[/v] - ω)[^]2[/^] + (ω[v]1[/v][^]2[/^])}

[TOP RIGHT NOTES:]

[image: of arrow]

μ[v]x[/v]' = Ŧ cos {backwards ⱸ} A sin ({backwards ʎ}t) + sin {backwards ⱸ}B

(μ[v]z[/v]')/(?) = Ŧ sin {backwards ⱸ} A sin ({backwards ʎ}t) ¤ cos {backwards ⱸ}B

μ[v]x[/v]' sin {backwards ⱸ} - (μ[v]{?}[/v]' cos {backwards ⱸ} = B

μ[v]x[/v]' cos {backwards ⱸ} + (μ[v]z[/v]'/{?}))' sin {backwards ⱸ} = A sin ωt

H'[v]x[/v] = H[v]1[/v]

H'[v]y[/v] = 0

H[v]z[/v]' = H[v]0[/v]

[BOTTOM LEFT NOTES:]
[image containing: multiplanar graph; H[v]1[/v]|Ɣ|; (ω-H[v]0[/v]|Ɣ|); ?; {backwards ʎ}; {backwards ⱸ};]

sin {backwards ⱸ} = [^][/^] (H[v]1[/v]|Ɣ|)/({backwards ʎ})

cos {backwards ⱸ} = (ω-(H[v]0[/v]|Ɣ|))/({backwards ʎ})

μ[v]x[/v]' = Ŧ cos {backwards ⱸ} (A sin ({backwards ʎ}t + ε) + B)

μ[v]z[/v]' = Ŧ sin {backwards ⱸ} (A sin ({backwards ʎ}t + ε) + B)

[BOTTOM RIGHT NOTES:]

Type II.

(μ[v]x[/v]')/(μ[v]z[/v]') = - (|Ɣ|H[v]0[/v]-ω)/(|Ɣ|H[v]1[/v]) = - δ

(d[^]2[/^]μ[v]y[/v]')/(d(t[^]2[/^])) = - ( (H[v]1[/v][^]2[/^]Ɣ[^]2[/^]) + (|Ɣ|H[v]0[/v]-ω)[^]2[/^] ) (μ[v]y[/v])'

μ[v]y[/v]' = A sin ({backwards ʎ}t)

μ[v]x[/v]' = +- (|Ɣ|H[v]0[/v]-ω)/({backwards ʎ}) A sin ({backwards ʎ}t) + ((|Ɣ|H[v]1[/v])/({backwards ʎ}))B

μ[v]z[/v]' = Ŧ (|Ɣ|H[v]1[/v])/({backwards ʎ}) A sin ({backwards ʎ}t) + ((|Ɣ|H[v]0[/v]-ω)/({backwards ʎ}))B