example_IV_2_01

example_IV_2_01 - Example IV.2.1 Find theparticular...

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Example IV.2.1 Find the particular solution  of the EOM for the system  shown  below  for  a=T/2 . f(t) F 0 -a/2 a/2 T Fourier Series   where   = 2 π /T  and       Therefore,   Remarks a) Since f(t) is an even function  of time, the sine components  of the Fourier   series make no contributions. b) Since the average value of f(t) is non-zero (positive), then   c) Since the magnitude  of the Fourier coefficients     go as:
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  we should  expect the convergence of the infinite series to be slow. d) If f(t) is a forcing that is applied  to a single-DOF damped  oscillator, the   particular solution  for the response of the oscillator will be:   where   Note that     goes as:   Therefore, the series for     goes as    . Therefore, the series for the response   converges more rapidly  than  the Fourier series for the excitation  f(t). For  not near an integer multiple of the fundamental  frequency 
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example_IV_2_01 - Example IV.2.1 Find theparticular...

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