Sr Examen
Ecuación diferencial mx''+cx'+ax=c*(-1.047*y/v)*(cos(1.047*v*t))+a(-y/v)*(sin(1.047*v*t))
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Solución
Ha introducido
[src]
/1047*t*v\ /1047*t*v\
2 a*y*sin|--------| 1047*c*y*cos|--------|
d d \ 1000 / \ 1000 /
a*x(t) + c*--(x(t)) + m*---(x(t)) = - ----------------- - ----------------------
dt 2 v 1000*v
dt
$$a x{\left(t \right)} + c \frac{d}{d t} x{\left(t \right)} + m \frac{d^{2}}{d t^{2}} x{\left(t \right)} = - \frac{a y \sin{\left(\frac{1047 t v}{1000} \right)}}{v} - \frac{1047 c y \cos{\left(\frac{1047 t v}{1000} \right)}}{1000 v}$$
a*x + c*x' + m*x'' = -a*y*sin(1047*t*v/1000)/v - 1047*c*y*cos(1047*t*v/1000)/(1000*v)
Respuesta
[src]
/ ____________\ / ____________ \
| / 2 | | / 2 |
t*\-c - \/ c - 4*a*m / t*\\/ c - 4*a*m - c/ 2 /1047*t*v\ 2 /1047*t*v\ /1047*t*v\ /1047*t*v\ /1047*t*v\ /1047*t*v\
------------------------ ----------------------- 1096209000000*y*c *sin|--------| 1000000000000*y*a *sin|--------| 1047000000000*a*c*y*cos|--------| 1047000000000*a*c*y*cos|--------| 1096209000000*a*m*v*y*sin|--------| 1147730823000*c*m*v*y*cos|--------|
2*m 2*m \ 1000 / \ 1000 / \ 1000 / \ 1000 / \ 1000 / \ 1000 /
x(t) = C1*e + C2*e - ------------------------------------------------- - ----------------------------------------------------- + ------------------------------------------------- - ----------------------------------------------------- + ------------------------------------------------- + -------------------------------------------------
2 / 2 \ 2 / 2 \ 2 2
/ 2\ 2 2 |/ 2\ 2 2| / 2\ 2 2 |/ 2\ 2 2| / 2\ 2 2 / 2\ 2 2
\1000000*a - 1096209*m*v / + 1096209000000*c *v v*\\1000000*a - 1096209*m*v / + 1096209000000*c *v / \1000000*a - 1096209*m*v / + 1096209000000*c *v v*\\1000000*a - 1096209*m*v / + 1096209000000*c *v / \1000000*a - 1096209*m*v / + 1096209000000*c *v \1000000*a - 1096209*m*v / + 1096209000000*c *v
$$x{\left(t \right)} = C_{1} e^{\frac{t \left(- c - \sqrt{- 4 a m + c^{2}}\right)}{2 m}} + C_{2} e^{\frac{t \left(- c + \sqrt{- 4 a m + c^{2}}\right)}{2 m}} - \frac{1000000000000 a^{2} y \sin{\left(\frac{1047 t v}{1000} \right)}}{v \left(1096209000000 c^{2} v^{2} + \left(1000000 a - 1096209 m v^{2}\right)^{2}\right)} + \frac{1047000000000 a c y \cos{\left(\frac{1047 t v}{1000} \right)}}{1096209000000 c^{2} v^{2} + \left(1000000 a - 1096209 m v^{2}\right)^{2}} - \frac{1047000000000 a c y \cos{\left(\frac{1047 t v}{1000} \right)}}{v \left(1096209000000 c^{2} v^{2} + \left(1000000 a - 1096209 m v^{2}\right)^{2}\right)} + \frac{1096209000000 a m v y \sin{\left(\frac{1047 t v}{1000} \right)}}{1096209000000 c^{2} v^{2} + \left(1000000 a - 1096209 m v^{2}\right)^{2}} - \frac{1096209000000 c^{2} y \sin{\left(\frac{1047 t v}{1000} \right)}}{1096209000000 c^{2} v^{2} + \left(1000000 a - 1096209 m v^{2}\right)^{2}} + \frac{1147730823000 c m v y \cos{\left(\frac{1047 t v}{1000} \right)}}{1096209000000 c^{2} v^{2} + \left(1000000 a - 1096209 m v^{2}\right)^{2}}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral