Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 9n°y = 3nd(t – 2), y(0) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L {y(t)} = b. Obtain the solution y(t). y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. %3D y(t) = if 0

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: