Find the Laplace transform by using the theorem of L{f(t-a)H(t-a)}=(e^-as)F(s)
L{(e^4t)H(t-10)}
To find the Laplace transform of the function (e^4t)H(t-10) using the given theorem, we can follow these steps:
Step 1: Identify the function and the shift value parameters in the given expression.
- The function is e^4t.
- The shift value is a = 10.
Step 2: Compute the Laplace transform of the original function, F(s).
- The Laplace transform of e^kt is 1 / (s - k).
- Applying this formula, the Laplace transform of e^4t is 1 / (s - 4).
Step 3: Use the given theorem to find the Laplace transform of (e^4t)H(t-10).
- According to the theorem, L{f(t-a)H(t-a)} = e^(-as) * F(s).
- Plugging in the values, we have:
L{(e^4t)H(t-10)} = e^(-4s) * (1 / (s - 4)).
Therefore, the Laplace transform of (e^4t)H(t-10) is e^(-4s) / (s - 4).