5_Chapter_2.pptx - MECHANICAL VIBRATION SINGLE DEGREE OF FREEDOM SYSTEMS Free Undamped Vibration Equation of Motion Newton's Law Energy Method 1 Forced

5_Chapter_2.pptx - MECHANICAL VIBRATION SINGLE DEGREE OF...

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MECHANICAL VIBRATION SINGLE DEGREE OF FREEDOM SYSTEMS Free Undamped Vibration Equation of Motion Newton's Law Energy Method 1
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Forced Vibration The general solution of this equation is given by the sum of the solutions for the homogeneous equation ( transient solution) and for the non homogeneous equation ( steady state solution). Since the homogeneous equation represents the free vibration, the solution for a damped system has been given previously. The particular solution (steady state solution) representing the solution for the non homogeneous equation, can be assumed to be in the form 2 F 0 sin t t sin F = k x + x c + x m 0 x X sin ( t - )
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the frequency ratio the Phase 4 X c = F (k - m 0 2 ) ( ) 2 2   tan c 1- (m -1 2 / / ) k k k m , , = c 2m r = ) r 2 ( ) r 1 ( k / F X 2 2 2 0 2 1 r 1 r 2 tan
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5 Substitute sin and cos back in (a) to get Therefore: The amplitude X can also be expressed in terms of , r, x st :
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