The Laplace transform of a unit-ramp function starting at t = a is
Question
The Laplace transform of a unit-ramp function starting at t = a is
Solution
The Laplace transform of a unit-ramp function starting at t = a is given by the formula:
L{u(t-a) * (t-a)} = e^(-as) / s^2
Here's the step-by-step solution:
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The Laplace transform of a unit-ramp function, t, is 1/s^2.
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If the function is delayed by a, i.e., it starts at t = a, we multiply the function by a unit-step function, u(t-a).
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The Laplace transform of a delayed function is given by multiplying the Laplace transform of the original function by e^(-as).
So, the Laplace transform of a unit-ramp function starting at t = a is e^(-as) / s^2.
Similar Questions
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