Engineering Dynamics

Mechanical Vibration

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Session Overview

Covered this week: The last several lectures deal with mechanical vibration. Up to now in the course considerable emphasis has been placed on finding equations of motion of mechanical systems. The study of vibration will emphasize the analysis of the solution of the equations of motion of a particularly important class of dynamics problems: the vibration of machines. Balance scales are simple tools that can give the mass of an object relative to another object through finding the equilibrium point. Image courtesy of Lichfield District Council on Flickr.

Assignments

Problems and Concept Questions

Each problem set has concept questions paired with most problems. Answers to the concept questions are handed in before the overall problem set is due. You should therefore answer the concept questions in each problem set while watching the video lectures for the week. Then, use the Concept Question Answer Key (below in the Check Yourself section) to check your work before continuing to work on the problem set.

Please note that if your answer to the concept question is incorrect, it is likely that you may start down an unproductive pathway to a solution. Try to fully understand the answer to the concept question before you begin the regular problem.

• Problem Set 9: Problems and Concept Questions (PDF)

Videos

Lecture Videos

• Watch Lecture 19: Introduction to Mechanical Vibration

  • Video Chapters
    • Introduction to the single degree of freedom (SDOF) system)
    • Finding the equation of motion with respect to the static equilibrium position
    • Response of the SDOF system to initial conditions
    • Meaning of phase angle in free decay
    • Engineers approach to the solution of the 2nd order differential equation with initial conditions
    • Estimation of natural frequencies and damping ratios from measured response: the logarithmic decrement

• Watch Lecture 20: Linear System Modeling a Single Degree of Freedom Oscillator

  • Video Chapters
    • Concept question discussion of Problem set 9-keep
    • Damped response of spring-mass-dashpot system to initial conditions
    • Finding the response of a pendulum to initial conditions
    • Example: Ballistic pendulum
    • Experimental determination of damping ratio
    • Steady state linear system response to harmonic input
    • Demonstration of a beam with a rotating mass shaker

Check Yourself

Concept Question Answer Key and Problem Set Solutions

The solutions are presented in two files, one with the answers to the concept questions, and one with solutions and in-depth explanations for the problems. Work the problems on your own and check your answers when you’re done.

• Problem Set 9: Concept Question Answer Key (PDF)
• Problem Set 9: Problem Solutions and Explanations (PDF)

Looking for something specific in this course? The Resource Index compiles links to most course resources in a single page.

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