R(s) \frac{\alpha}{s} \frac{1}{(s+1)} C(s) From the figure shown obtain the following: - The value of \alpha having a damping ratio of 0.5.
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The transfer function of the system is given by the ratio of the Laplace transform of the output to the Laplace transform of the input. In this case, the transfer function is given by: G(s) = R(s) / C(s) = 1 / (s+1) Show more…
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The damping constant $(c)$ of the dashpot shown in Fig. 1.108 is given by [1.27]: $$ c=\frac{6 \pi \mu l}{h^{3}}\left[\left(a-\frac{h}{2}\right)^{2}-r^{2}\right]\left[\frac{a^{2}-r^{2}}{a-\frac{h}{2}}-h\right] $$ Determine the damping constant of the dashpot for the following data: $\mu=0.3445 \mathrm{~Pa}-\mathrm{s},$ $l=10 \mathrm{~cm}, h=0.1 \mathrm{~cm}, a=2 \mathrm{~cm}, r=0.5 \mathrm{~cm}$
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