Introducció

(TBD)

Fórmules matemàtiques

Editor onlined de fórmules matemàtiques:

• https://www.codecogs.com/latex/eqneditor.php?lang=es-es

Uns quants exemples de fórmules i equacions que utilitzo en el llibre:

dp/dt = -am (1)
dm/dt  = bp (2)

\frac{dp}{dt}= -am
\frac{dm}{dt}= bp

d2m/dt2 = -ab m (3)
\frac{d^2 m}{dt^2}= -ab\ m

m(t) = A sin (wt + phi) (4)
m(t) = A\ sin (\omega t + \varphi)

w = sqrt(ab) (5)
w = \sqrt{ab}

T = 2*pi/w = 2*pi/sqrt(ab) (6)
T = \frac{2\pi}{\omega} 

A = mo/w = mo / sqrt(ab) (7)
A = \frac{m_o}{\omega} = \frac{m_o}{\sqrt{ab}}
 

p(t) = Aw cos (wt + phi) = Bcos (wt + phi) (8)
p(t) = A\omega\ cos(\omega t + \varphi) = B\ cos(\omega t + \varphi)

B = sqrt(a/b) A = mo/b (9)
B = \sqrt{\frac{a}{b}}\ A = \frac{m_o}{b}

sin^2(wt + phi) + cos^2(wt + phi) = 1 (10)
sin^2(\omega t + \varphi) + cos^2(\omega t + \varphi) = 1

m^2/A^2 + p^2/B^2 = 1 (11)
\frac{m^2}{A^2} + \frac{p^2}{B^2} = 1


m = +- A/B sqrt (B^2 - p^2) (12)
m = \pm \frac{A}{B}\ \sqrt{B^2 - p^2}

m = +- 1.66 sqrt (9 - p^2) (13) 
m = \pm 1.66\ \sqrt{9 - p^2}

1/2 ab m^2 = 1/2 A^2 w^2 cos^2(wt + phi) + 1/2 ab A^2 sin^2 (wt + phi) = 1/2 A^2 ab (sin^2 + cos^2) = 1/2 A^2 ab = 1/2 mo ^ 2 (14)
\frac{1}{2}\ ab\ m^2 = \frac{1}{2}\ A^2\ \omega^2\ cos^2(\omega t + \varphi)\ +\ \frac{1}{2}\ ab\ A^2\ sin^2(\omega t + \varphi) = \\ = \frac{1}{2}\ A^2\ ab\ (sin^2(\omega t + \varphi) + cos^2(\omega t + \varphi)) = \frac{1}{2}\ A^2\ ab\ = \frac{1}{2}\ m_o^2

dp/dt = A11p + A12m (15)
\frac{dp}{dt}= A_1_1p + A_1_2m

dm/dt = A21p + A22m (16)
\frac{dm}{dt}= A_2_1p + A_2_2m

(A11 A12
A21 A22)   (17)
\begin{pmatrix}
A_1_1 & A_1_2 \\
A_2_1 & A_2_2 \\
\end{pmatrix}

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creat per Joan Quintana Compte, novembre 2018