Question

A forced damped harmonic oscillator with natural frequency \omega 0, has an applied periodic force F (t) = 0, for nT < t <= (n +( 1)/(2))T (1) and F (t) = F0, for (n +( 1)/(2))T < t <= (n + 1)T, (2) where T = 6(\pi )/(\omega )0 and n = 0, 1, 2, ... (a) Find the fourier series representation of the force in terms of the coefficients an and bn with \omega n = n\omega . (b) Find the particular solution response xp(t) in terms of the amplitudes An and phases \delta n with a damping coefficient given by \beta .

          A forced damped harmonic oscillator with natural
frequency \omega 0, has an applied periodic force
F (t) = 0, for nT < t <= (n +( 1)/(2))T (1)
and
F (t) = F0, for (n +( 1)/(2))T < t <= (n + 1)T, (2)
where T = 6(\pi )/(\omega )0 and n = 0, 1, 2, ... (a) Find the fourier series
representation of the force in terms of the coefficients an and bn
with \omega n = n\omega . (b) Find the particular solution response xp(t) in
terms of the amplitudes An and phases \delta n with a damping coefficient
given by \beta .

Added by John T.

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