Question

14. The mass-spring-damper system in Figure Q14 can be described by the differential equation $\frac{d^2x}{dt^2} + 2\zeta\omega\frac{dx}{dt} + \omega^2x = f(t)$ with the forcing term $f(t)$, the damping parameter $\zeta = \frac{c}{2\sqrt{(km)}} \ge 0$ and the radian frequency of free oscillation $\omega = \sqrt{\frac{k}{m}} > 0$. If the forcing term is a periodic function $f(t)$ with amplitude 2 and Fourier series $FS\{f(t)\} = \frac{6}{\pi} \sum_{n=1}^{\infty} \frac{3}{(4n-1)^3}cos((4n-3)\Omega t)$ and the damping parameter is set to $\zeta = 0$ which of the following options is true? A. A periodic solution does not exist for $\Omega = \omega$. B. The periodic solution of the mass-spring-damper system under the given forcing has an amplitude of 2 for all values of $\omega$. C. A periodic solution does not exist for $\Omega = \frac{3}{4}\omega$. D. The periodic solution has a finite number of harmonics.

          14. The mass-spring-damper system in Figure Q14 can be described by the differential equation
$\frac{d^2x}{dt^2} + 2\zeta\omega\frac{dx}{dt} + \omega^2x = f(t)$
with the forcing term $f(t)$, the damping parameter $\zeta = \frac{c}{2\sqrt{(km)}} \ge 0$ and the radian
frequency of free oscillation $\omega = \sqrt{\frac{k}{m}} > 0$.

If the forcing term is a periodic function $f(t)$ with amplitude 2 and Fourier series
$FS\{f(t)\} = \frac{6}{\pi} \sum_{n=1}^{\infty} \frac{3}{(4n-1)^3}cos((4n-3)\Omega t)$
and the damping parameter is set to $\zeta = 0$ which of the following options is true?
A. A periodic solution does not exist for $\Omega = \omega$.
B. The periodic solution of the mass-spring-damper system under the given forcing has
an amplitude of 2 for all values of $\omega$.
C. A periodic solution does not exist for $\Omega = \frac{3}{4}\omega$.
D. The periodic solution has a finite number of harmonics.

$14. The mass-spring-damper system in Figure Q14 can be described by the differential equation (d^2x)/(dt^2) + 2ζω(dx)/(dt) + ω^2x = f(t) with the forcing term f(t), the damping parameter ζ = (c)/(2√((km)))≥ 0 and the radian frequency of free oscillation ω = √((k)/(m)) > 0. If the forcing term is a periodic function f(t) with amplitude 2 and Fourier series FS{f(t)} = (6)/(π)∑n=1^∞(3)/((4n-1)^3)cos((4n-3)Ω t) and the damping parameter is set to ζ = 0 which of the following options is true? A. A periodic solution does not exist for Ω = ω. B. The periodic solution of the mass-spring-damper system under the given forcing has an amplitude of 2 for all values of ω. C. A periodic solution does not exist for Ω = (3)/(4)ω. D. The periodic solution has a finite number of harmonics.$

Added by Jenna B.

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