SOLID MECHANICS DYNAMICS TUTORIAL …

1 SOLID MECHANICS DYNAMICS TUTORIAL NATURAL VIBRATIONS ONE DEGREE OF FREEDOM This work covers elements of the syllabus for the Engineering Council Exam D225 DYNAMICS of Mechanical Systems, C105 Mechanical and Structural Engineering and the Edexcel HNC/D module Mechanical Science. Oscillations with two degrees of freedom are covered in other tutorials and these are vital for those sitting exam D225. On completion of this TUTORIAL you should be able to do the following. Explain the meaning of degrees of freedom . Define and explain Simple Harmonic Motion. Explain the meaning of free vibrations. Show how various systems vibrate with simple harmonic motion. Determine the natural frequency and periodic time for simple systems. Determine the displacement, velocity and acceleration of bodies vibrating with simple harmonic motion. Explain the use of energy to analyse vibrations (Rayleigh s Method) Explain how to combine several natural frequencies (Dunkerley s Method) This TUTORIAL covers the theory of natural vibrations and brings together other areas of studies in the process.

1.2 FREE VIBRATIONS- EXAMPLES A free vibration is one that occurs naturally with no energy being added to the vibrating system. The vibration is started by some input of energy but the vibrations die away with time as the energy

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