Correct Answer - Option 4 :
\(V(s) = \frac{{10}}{{{s^2} + 100}}\)
Concept:
L [f(t)] = F(s)
L [sin(at) u(t)] ↔ \(\frac{a}{{{s^2} + {a^2}}}\)
Application:
With v(t) = sin (10t) u(t), the Laplace transform will be:
\(V(s) = \frac{{10}}{{{s^2} + 100}}\)
Some common Laplace transforms are:
f(t)
|
F(s)
|
ROC
|
δ (t)
|
1
|
All s
|
u(t)
|
\(\frac{1}{s}\)
|
Re (s) > 0
|
t
|
\(\frac{1}{{{s^2}}}\) |
Re (s) > 0
|
tn
|
\(\frac{{n!}}{{{s^{n + 1}}}}\) |
Re (s) > 0
|
e-at
|
\(\frac{1}{{s + a}}\) |
Re (s) > -a
|
t e-at
|
\(\frac{1}{{{{\left( {s + a} \right)}^2}}}\) |
Re (s) > -a
|
tn e-at
|
\(\frac{{n!}}{{{{\left( {s + a} \right)}^n}}}\) |
Re (s) > -a
|
sin at
|
\(\frac{a}{{{s^2} + {a^2}}}\) |
Re (s) > 0
|
cos at
|
\(\frac{s}{{{s^2} + {a^2}}}\) |
Re (s) > 0
|