All problems refer to the mass–spring

Chapter 4, Problem 13E

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QUESTION:

Show that for the underdamped system of Example 3 , the times when the solution curve \(y(t)\) in (33) touches the exponential curves \(\pm \sqrt{7 / 12} e^{-2 t}\) are not the same values of  for which the function \(y(t)\) attains its relative extrema.

Equation Transcription:

Text Transcription:

y(t)

+/- sqrt{7/12} e^{-2 t}

y(t)

Questions & Answers

QUESTION:

Show that for the underdamped system of Example 3 , the times when the solution curve \(y(t)\) in (33) touches the exponential curves \(\pm \sqrt{7 / 12} e^{-2 t}\) are not the same values of  for which the function \(y(t)\) attains its relative extrema.

Equation Transcription:

Text Transcription:

y(t)

+/- sqrt{7/12} e^{-2 t}

y(t)

ANSWER:

Solution:

Step 1:

In this question it is required to show that the times when the solution curve  in equation (33) touches the exponential curves are not same as the values of  for which the function  attains its relative extrema.

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