<急>誰會工程數學第二移位定理？

3.￡{exp(-2s)/(s^2+9)} = ?

Formula-1: ￡{exp(-as)/s} = u(t-a)

Formula-2: ￡{exp(-as)*F(s)} = f(t-a)*u(t-a)}


￡{F(s)} = ￡{1/(s^2+9)} = sin(3t)

=> ￡{exp(-2s)/(s^2+9)} = sin[3(t-2)]*u(t-2) = sin(3t-6)*u(t-2)




2.￡{exp(-21s)/[s(s^2+16)]}

= ￡{exp(-21s)[1/s - 1/(s^2+16)]/16}

= ￡{exp(-21s) * 1/16s} - ￡{exp(-21s) * 1/(s^2+16)/16}

= u(t-21)/16 - sin[4(t-21)]*u(t-21)/16

= [1 - sin(4t-84)]*u(t-21)/16





1.f(t) = t-2, 0 <= t <16; f(t) = -1, t>=16

w = F(s)

= ∫(0~16)(t-2)exp(-st)dt + ∫(16~oo)exp(-st)dt

=-∫(0~16)t*d[e^(-st)]/s+2∫(0~16)d[e^(-st)]/s-∫(16~oo)d[e^(-st)]/s

= -A + B - C


A = t*e^(-st) - ∫e^(-st)dt

= t*e^(-st) + e^(-st)/s ;;; t = 0~16

= 16*e^(-16s) + e^(-16s)/s - 1/s


B = 2*e^(-st)/s ;;; t = 0~16

= 2*e^(-16s)/s - 2/s


C = e^(-st)/s ;;; t = 16~oo

= -e^(-16s)/s



w = -16*e^(-16s) - e^(-16s)/s + 1/s + 2*e^(-16s)/s - 2/s + e^(-16s)/s

= -16*e^(-16s) + 2*e^(-16s)/s - 1/s