Aufgaben zur Automatisierungstechnik
Laplacetransformation
(T.WAIBL, Abteilung Elektrotechnik, HTL-Anichstraße, Innsbruck)
Funktion im Zeitbereich f(t) | Lösung: F(s) | |
5 | t³ | 6/s4 |
6 | tn | n! / sn+1 |
7 | 3(t-3)² | 3/s³ * (2-6s+9s²) |
8 | (t+1)²-(t-1)² | f(t)=4t; F(s)=4/s² |
9 | 3(t+2)²-2(t-3)² | 2/s³ * (1+12s-3s²) |
10 | eat | 1/(s-a) |
11 | ejwt | 1/(s-jw) |
12 | e(a+jw)t | 1/(s-a-jw) |
13 | 2-e3t | (s-6) / (s(s-3)) |
14 | 2+6t+4t²-2e3t | -(10s+24) / (s³(s-3)) |
15 | teat | 1 / (s-a)² |
16 | 1/a² * [1+(at-1)eat] | 1 / [s(s-a)²] |
17 | e-jwt / (jw) | 1 / [w(js-w)] |
18 | 1/a * e-t/a | 1 / (1+as) |
19 | 1/a * (eat-1) | 1 / [s(s-a)] |
20 | 1/a² * (eat-at-1) | 1 / [s²(s-a)] |
21 | (1-e-t/a) | 1 / [s(as+1)] |
22 | ae-t/a+t-a | 1 / [s²(as+1)] |
23 | 1/(ab) * [1+(beat-aebt)/(a-b)] | 1 / [s(s-a)(s-b)] |
24 | sin(wt) | w / (s²+w²) |
25 | cos(wt) | s / (s²+w²) |
26 | Ae-atsin(wt) | A / [(s+a)²+w²] |
27 | Ae-atcos(wt) | A * (s+a) / [(s+a)²+w²] |
28 | sin(wt+j) | ( w cosj + s sinj ) / (s²+w²) |
31 | (t-3)²; f(t)=0 für t<3 | e-3s * 2 / s³ |
32 | (t-a)³; f(t)=0 für t<a | e-as * 6 / s4 |
33 | sinw(t-T/4); f(t)=0 für t<T/4 | e-Ts/4 * w / (s²+w²) |
34 | e(t-a); f(t)=0 für t<a | e-as / (s-1) |