Question 3. Consider the following statement: \"The impulse response is obtained

Question

Question 3. Consider the following statement: "The impulse response is obtained from the free response by setting the initial displacement to zero and the initial velocity to (1/m)." In your own words, explain this statement in a clear and concise manner. Your explanation should contain the following elements: the definition of the impulse response; the reasons for treating the impulse response as a free response; and the justification for selecting these specific values for the initial conditions. Sketch diagrams if necessary. (3 Points) 93 The concept of the impulse response is a crucial one in vibrations. Please study the textbook and lecture notes carefully to learn this concept thoroughly. This question (or a closely related variation) will appear again in the Final Examination.

Explanation / Answer

Whenever a system (block) or signal is given an input signal, it alters or process the input to give desired output signal depending upon the system transfer function.

The output of the system to a unit input signal is the impulse response of the system.

Free response is the response where interchange of the energies takes place i.e kinetic energy to potential energy or vice versa. For example in spring mass system, a free response is achieve when displacement of the spring is interchange by the velocity I.e potential energyis converted into kinetic energy or vice versa. That is why impulse response is also sometime called as free response because here here unit input will give a desired output.

In the above statement, it is actually the area of a rectangular pulse at x = 0, whose width is considered to be tending to zero (negligible width).

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