2. Consider an undamped oscillator which moves a certain mass. The mov

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2. Consider an undamped oscillator which moves a certain mass. The movement of the mass can be described by the equation below, where δ(t) represents the Dirac Delta function. y′′ − 9y = δ(t) with y(0) = 0 and y′(0) = 0. (a) ( 8 points) Find the solution function, y(t), for this differential equation using Laplace transforms. (b) (2 points) In the case given by the problem, the Dirac Delta function applies an instantaneous force (impulse) at time t = 0. Write a differential equation to represent the situation if the impulse were instead applied at time t = π.

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Consider an undamped oscillator which moves a certain mass. The movement of the mass can be described by the equation below, where $δ (t)$ represents the Dirac Delta function.

y^{''} - 9 y = δ (t)

with

y (0) = 0

and

y^{'} (0) = 0

. (a) ( 8 points) Find the solution function,

y (t)

, for this differential equation using Laplace transforms. (b) (2 points) In the case given by the problem, the Dirac Delta function applies an instantaneous force (impulse) at time