Iutpc

Transformada de laplace

L
F(x)
F(s)

L [f (t)] = f(s) = 0∞e-stfe, dz

L (c)= f(t)

U(t)

t

f f(t)



t



f(t)= t2 F(t)




tL [f (t)] = f(s) = 0∞e-stf(t)dt= L ----- 0te-stft dt limt→∞0te-stf(t) dt
T ∞
L (c) = csL (t) = 1s2

ea = cosa+jsina j
s= - v± jB
B

real
voperar con una variable compleja
w=2πf
Representación implícita
f(x)

f(x)

x

M1
M2R2= 12T B2=dy2dtu
M2

K2 B2

K1= (Y1-Y2) B1= dy1dt-dy2dt
Y2(t)
K1 B1
M1


T f(t) Y1(t)

F(t)= M1x dy12(t)dt2 + B1 (dy1(t)dt- dy2(t)dt) + K1 (y1(t) – y2(t) )
0= M2 dy2(t)dt2 + B2 ( dy2(t)dt ) + K2Y2(t) – B1 ( dy1(t)dt - dy2(t)dt ) – K1 (y1- y2)

L (df(t)dt )= 0∞e-stdf(t)dt (dt) = [e-stF(t)]∞0+ s 0∞e-stFtdt
L [d2Ftdt2] =0∞e-std2F(t)dt2 dt = [ e-stdf(t)dt]∞0+ s 0∞e-stdf(t)dtdt
L [ d2f(t)dt2 ] = s [ sf (s) ] = s2 f(s)

G(t) = 0tftdt campo R. Campo C.
L [ g(t) ] =0∞e-st0tftdtdt (t) (s)
dg(t)dt = f(t) L [ dy(t)dt ] = 0∞e-stftdtF(t)= M1 d2y1(t)dt2+ B1 (dy1dt- dy(t)dt ) + K1 [ y(t) – y2 (t)]
F(s) = M1 s2 y1(s) + B1s [ y1(s) – y2(s)]
0= M2 s2 y2(s) + K2y2(s) + B2s y2(s) – K1[Y1(s)-Y2(s)] – B1 s [ y1(s)-y2(s)]
y(s)f(s)= ?

Ejercicio:
* F(t)= 3t+2e3t
L [ f(t)] =? L(3t+2e3t=3Lt+ 2 L (e3t)= 3 1s2+ 21s3=3s2+ 2s-3

Lt=1s2...