Exercise · ZW-UNIT-STEP-FUNCTION-006 · ★★☆ Intermediate
What is \(\mathcal L\{u_1(t)\sin(t-1)\}\)?
Choose one option.
Show answer
- B. \(\dfrac{e^{-s}}{s^2+1}\)
Explanation
The argument \(t-1\) matches the delay of the step, so the theorem applies directly: \(e^{-s}\) times the transform of \(\sin t\).
Review the concept: Unit step function
The unit step function \(u_c(t)\), with \(c\ge0\), equals 0 while \(t<c\) and equals 1 from \(t=c\) on; it is a switch that turns on at time \(c\).
\[u_c(t)=\begin{cases}0,&t
More practice problems: unit step function
- ZW-UNIT-STEP-FUNCTION-001 What is mathcal L\u_3(t)\?
- ZW-UNIT-STEP-FUNCTION-002 What is mathcal L\u_2(t) (t-2)\?
- ZW-UNIT-STEP-FUNCTION-003 If F(s)=mathcal L\f\ and c≥0, what is mathcal L\u_c(t) f(t-c)\?
- ZW-UNIT-STEP-FUNCTION-004 Write, using steps, the function equal to 2 for t<4 and 5 for t≥4.
- ZW-UNIT-STEP-FUNCTION-005 What is mathcal L\u_1(t)-u_3(t)\?
- ZW-UNIT-STEP-FUNCTION-007 What is mathcal L^-1\(e^-4s)/(s+1)\?
- ZW-UNIT-STEP-FUNCTION-008 What is mathcal L\t u_2(t)\? (Careful: the factor is t, not t-2.)
- ZW-UNIT-STEP-FUNCTION-009 The solution of y'+y=u_1(t), y(0)=0, is y=u_1(t)bigl(1-e^-(t-1)bigr). What is y(2)?