Final answer:
The question pertains to finding the response of a mechanical or control system to an impulse force using engineering techniques such as differential equations and Laplace transforms, and plotting the result. Parts of the question are unrelated to the required solution method.
Step-by-step explanation:
The question involves solving a differential equation to find the response of a system characterized by a given dynamic equation in the presence of an initial condition and external forces. In this case, it appears to be related to a mechanical or control system, and the presence of a delta function indicating an impulse suggests it could be a problem from a signals and systems or control systems course within an engineering curriculum.
The given information seems to have some parts that do not relate directly to computing the solution to the differential equation at hand. Regardless, to compute the response, one would typically use techniques such as the Laplace transform, taking into account the initial conditions of the system. Then, solving for the inverse Laplace transform would yield the solution in the time domain. The provided snippets of information also hint at evaluating the solution at certain time points, which is common in step-by-step problem-solving in engineering.
As for plotting the response, typically one would use software like MATLAB or Python libraries such as NumPy and Matplotlib to generate the plot, which is critical in visualizing the behavior of the system in response to the input forces over time.