A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium that exerts a viscous resistance of 45 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.Suppose the object is displaced an additional 0.05 mm and released.Find an function to express the object's displacement from the spring's natural position, in mm after tt seconds. Let positive displacements indicate a stretched spring, and use 9.8 ms2ms2 as the acceleration due to gravity.u(t) = 5·10−5(e−3t)sin(349.98t+π2)mIncorrect syntax error. Check your variables - you might be using an incorrect one.Submit QuestionQuestion 1 ### Spring-Mass-Damper System Analysis#### Problem DescriptionA mass of \( 1.25 \, \text{kg} \) stretches a spring \( 0.08 \, \text{m} \). The mass is in a medium that exerts a viscous resistance of \( 45 \, \text{N} \) when the mass has a velocity of \( 6 \, \frac{\text{m}}{\text{s}} \). The viscous resistance is proportional to the speed of the object.Suppose the object is displaced an **additional** \( 0.05 \, \text{m} \) and released.#### ObjectiveFind a function to express the object's displacement from the spring's **natural position**, in meters, after \( t \) seconds. Let positive displacements indicate a stretched spring, and use \( 9.8 \, \frac{\text{m}}{\text{s}^2} \) as the acceleration due to gravity.#### Solution AttemptThe attempt to derive the displacement function resulted in the following:\[ u(t) = 5 \cdot 10^{-5} (e^{-3t}) \sin \left( 349.98t + \frac{\pi}{2} \right) \, \text{m}\]However, this equation contains a **syntax error**. There might be an incorrect variable or a miswritten expression. Please double-check the formula, variables, and their corresponding values to ensure accuracy.

Answered: A mass of 1.25 kg stretches a spring…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium that exerts a viscous resistance of 45 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.

Suppose the object is displaced an additional 0.05 mm and released.

Find an function to express the object's displacement from the spring's natural position, in mm after tt seconds. Let positive displacements indicate a stretched spring, and use 9.8 ms2ms2 as the acceleration due to gravity.

u(t) = 5·10−5(e−3t)sin(349.98t+π2)mIncorrect syntax error. Check your variables - you might be using an incorrect one.

Submit QuestionQuestion 1