Laplace transforms ramp function

Let us now apply the definition of the Laplace transformation to some important time functions steps, ramps, exponential, sines, etc. 

LAPUCE-DOUAIM DYNAMICS AND OONTKOL Therefore the Laplace transformation of a ramp function is... 

Now consider a ramp function described by fit) — t[u t) The Laplace transform of this function is /s. Finally, the Laplace transform of a sine-wave disturbance, sin(cuf)> is co/(j + of). 

Ramp function, 130 Laplace transform, 130 as the response of pure integrator, 178-79... 

Z(w) = 1/wC, and in the s-domain Z(s) = 1/sC. The Laplace transforms of some very important excitation waveforms are very simple for example, for a unit impulse it is 1, a unit step function 1/s, a ramp 1/s, etc. That is why the excitation with, for example, a unit impulse is of special interest examining the response of a system. In the extended immittance definition, calculations with some nonsinusoidal waveforms become very simple. Even so, Laplace transforms are beyond the scope of this book. 

The generation of such a forcing function is used in steering theory as well as in adiabatic and scanning calorimetry. The ramp function has the following Laplace transform ... 

For several types of time function, such as pulse, step, ramp, wave changes, the Laplace transformations are shown in Table 5.1. The time functions belonging to a particular Laplace transform are given in Table 5.2. 

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