left to fall from rest on the tabletop. Deduce an expression for the velocity at which the ball will bounce back off the tabletop. On its way back, will the mass bounce back to its initial height? If it will not, where will the difference in energy go?

left to fall from rest on the tabletop. Deduce an expression for the velocity at which the ball will bounce back off the tabletop. On its way back, will the mass bounce back to its initial height? If it will not, where will the difference in energy go?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Question

A steel ball of mass M is held at a distance H above
a massless rigid tabletop supported by undamped
springs whose equivalent stiffness is K. If the ball is
left to fall from rest on the tabletop. Deduce an
expression for the velocity at which the ball will
bounce back off the tabletop. On its way back, will
the mass bounce back to its initial height? If it will
not, where will the difference in energy go?
Discuss mathematically! (Pls solve the question in
detail with figure)

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Step 1: Draw the schematic diagram for spring-mass system.

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Step 2: Write the equation for total energy of the system at initial releasing time.

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Step 3: Write the equation for total energy of the system at final compressed state.

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Step 4: Write the equation for total energy of the system at time when ball bounce back off the table.

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Step 5: Deduce the expression for velocity at which the ball bounce back off the table .

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Step 6: Calculate the final height reached by the ball using kinematic equation.

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