Using the Laplace transform table in the video (data sheet), the Laplace transform of is:

Question

Using the Laplace transform table in the video (data sheet), the Laplace transform of  is:

BlackTom AI · Accepted Answer

The question as provided is incomplete: it mentions using the Laplace transform table and asks for the Laplace transform of an unspecified function. The answer options are not listed, so we cannot compare multiple choices.

However, the given answer text appears to be 's / (s^2 + ω^2)', which corresponds to the Laplace transform of cos(ω t), i.e., L{cos(ω t)} = s / (s^2 + ω^2) for Re(s) > 0. If the original function were cos(ω t), then this form is correct because the transform of cos is derived from the definition L{f(t)} = ∫_0^∞ e^(-st) cos(ω t) dt, yielding s/(s^2 + ω^2).

To evaluate or justify transforms in general, one would:
- Identify the time-domain function x(t) whose Laplace transform is sought.
- Recall standard pairs from the table, e.g., L{1} = 1/s, L{cos(ωt)} = s/(s^2+ω^2), L{sin(ωt)} = ω/(s^2+ω^2).
- Check the region of convergence: for cos and sin transforms, Re(s) > 0 is typical, though more specific conditions may apply depending on damping.

If the intended function was not cos(ωt), then this expression would be incorrect for that function. For example:
- If the function were sin(ωt), the transform would be ω/(s^2 + ω^2).
- If the function were e^(αt) cos(ωt), the transform would be (s - α)/((s - α)^2 + ω^2).

Since the options are missing, there is no way to determine which choice is correct beyond confirming that s/(s^2+ω^2) is the standard transform for cos(ωt).Ensure the original function in the question is correctly identified before selecting or confirming this as the answer.

AMME2000 BMET2960 BMET9960 (ND) Week 11 Pre-work

Using the Laplace transform table in the video (data sheet), the Laplace transform of is:

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