Penjelasan dengan langkah-langkah:

1.     f(t) = vo.t + 0,5.a.t^2

F(s) = L{f(t)} = ∫(e^(-st).f(t)) dt

= ∫(e^(-st).(vo.t + 0.5.a.t^2)) dt

= vo/s ∫(e^(-st).t) dt + (a/2s^2) ∫(e^(-st).t^2) dt

= vo/s( -(1/s^2) e^(-st).t + 1/s e^(-st)) + (a/2s^2) ( -(1/s^3) e^(-st).t^2 + 1/s^2 e^(-st).t )

= (vo/s^2 + a/2s^3) e^(-st)

F(s) = (vo/s^2 + a/2s^3)

2.     f(t) = A.sin(w.t)

F(s) = L{f(t)} = ∫(e^(-st).f(t)) dt

= A.∫(e^(-st).sin(w.t)) dt

= A/s.∫(e^(-st).sin(w.t)) dt

= A/s( -(1/s^2+w^2) e^(-st).cos(w.t) + 1/(s+w) e^(-st).sin(w.t) )

= A/(s^2+w^2)

F(s) = A/(s^2+w^2)

3.     f(t) = A.sin (2.pi.f - w.t)

F(s) = L{f(t)} = ∫(e^(-st).f(t)) dt

= A.∫(e^(-st).sin (2.pi.f - w.t)) dt

= A/s.∫(e^(-st).sin (2.pi.f - w.t)) dt

= A/s( -(1/s+w) e^(-st).cos (2.pi.f - w.t) + 1/(s+w) e^(-st).sin (2.pi.f - w.t) )

= A/(s+w) (1 - e^(-s/w))

F(s) = A/(s+w) (1 - e^(-s/w))

Jadikan jawaban terbaik