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Laplace transform of unit ramp function H(t)

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The unit ramp function H(t) is defined by
H(t) =
0 t < 0
t t > 0

a) Determine the Laplace transform of H(t)
b) Solve the ODE y''+y = H(t −1) y(0) = 0 y'(0) = 0 
using
 Laplace
 transforms.


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The solution explains how to determine the Laplace transform of the unit ramp function H(t).

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(a) To find the Laplace transform H(s) of a step function H(t) substitute H(t) into the definition of the Laplace ...

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