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Question 5 20 pts A mass- spring- damper system is subjected to the periodic force shown. The mass of the system is m=10kg, the constant of the spring is 10000N/m and the constant of the damper is 500Ns/m. The period of the force is $\tau$ = 1 sec, and the amplitude A= 10N (a) If the Fourier transform approximation is given by: $f(t) = \frac{A}{2} - \frac{A}{\pi} \sum_{j=1}^{\infty} (\frac{1}{j} \sin(\frac{2\pi j}{\tau} t))$ Therefore, the expansion considering four terms is given by: $f(t) = \frac{A}{2} - \frac{A}{\pi} \sin(\frac{2\pi}{\tau} t) - \frac{A}{2\pi} \sin(\frac{4\pi}{\tau} t) - \frac{A}{3\pi} \sin(\frac{6\pi}{\tau} t)$ What is the maximum amplitude of the response corresponding to the four term of the Fourier approximation? Justify your answer. O 0.500 mm O 0.315 mm O 0.151 mm O 0.093 mm

          Question 5
20 pts
A mass- spring- damper system is subjected to the periodic force shown. The mass of the system is m=10kg, the constant of the spring is 10000N/m and the constant of the damper is 500Ns/m. The period of the force is $\tau$ = 1 sec, and the amplitude A= 10N

(a)
If the Fourier transform approximation is given by:
$f(t) = \frac{A}{2} - \frac{A}{\pi} \sum_{j=1}^{\infty} (\frac{1}{j} \sin(\frac{2\pi j}{\tau} t))$
Therefore, the expansion considering four terms is given by:
$f(t) = \frac{A}{2} - \frac{A}{\pi} \sin(\frac{2\pi}{\tau} t) - \frac{A}{2\pi} \sin(\frac{4\pi}{\tau} t) - \frac{A}{3\pi} \sin(\frac{6\pi}{\tau} t)$
What is the maximum amplitude of the response corresponding to the four term of the Fourier approximation? Justify your answer.

O 0.500 mm
O 0.315 mm
O 0.151 mm
O 0.093 mm

question 5 20 pts a mass spring damper system is subjected to the periodic force shown the mass of the system is m10kg the constant of the spring is 10000nm and the constant of the damper is 25088

Added by Thomas C.

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