Question

Find the inverse laplace transform of 2(1-e⁻ˢ)/s(1-e⁻³ˢ)

Answer 1

To find the inverse Laplace transform of 2(1-e⁻ˢ)/s(1-e⁻³ˢ), we can use partial fraction decomposition. The inverse Laplace transform of 2(1 - e⁻ˢ)/s(1 - e⁻³ˢ) is 2[1 - e⁻³ˢ].

Step-by-step explanation:

To find the inverse Laplace transform of 2(1-e⁻ˢ)/s(1-e⁻³ˢ), we can use the Laplace transform table. In the table, we have the Laplace transform of 1 - e⁻ˣ as 1/s. Applying this property, we can write the given expression as 2/s(1 - e⁻³ˢ).

Now, we can use partial fraction decomposition to split this expression. We can write 1 - e⁻³ˢ as (1/s) - (e⁻³ˢ/s). Therefore, the expression becomes 2 * [(1/s) - (e⁻³ˢ/s)] / s.

Now, we can take the inverse Laplace transform of each term separately using the Laplace transform table. The inverse Laplace transform of 1/s is 1 and the inverse Laplace transform of e⁻³ˢ/s is e⁻³ˢ. Therefore, the inverse Laplace transform of 2(1 - e⁻ˢ)/s(1 - e⁻³ˢ) is 2 [1 - e⁻³ˢ].