uependng on WIIeunei une interval is open or closed.) DE Find the resonant frequency o, for D = 0.283. (Use decimal. notation. Give your answer to three decimal places.) Hz w, R

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uepenung on WIieunei ue
interval is open or closed.)
DE
Find the resonant frequency o, for D = 0.283.
(Use decimal. notation. Give your answer to three decimal places.)
Hz
Transcribed Image Text:uepenung on WIieunei ue interval is open or closed.) DE Find the resonant frequency o, for D = 0.283. (Use decimal. notation. Give your answer to three decimal places.) Hz
The response of a circuit or other oscillatory system to an input of frequency w ("omega") is described by the function
() =
V(a - w) + 4Da
Both on (the natural frequency of the system) and D (the damping factor) are positive constants. The graph of o is called a
resonance curve, and the positive frequency w, > 0, where o takes its maximum value, if it exists, is called the resonant
frequency.
2
Let o = 0.8 Hz. Find the values of D for which the resonant frequency exists.
(Use symbolic notation and fractions where needed. Give your answers as intervals in the form (, ). Use the symbol co for
00
infinity and u for combining intervals, and the appropriate type of parenthesis " (", ") ", "[".") " depending on whether the
interval is open or closed.)
Transcribed Image Text:The response of a circuit or other oscillatory system to an input of frequency w ("omega") is described by the function () = V(a - w) + 4Da Both on (the natural frequency of the system) and D (the damping factor) are positive constants. The graph of o is called a resonance curve, and the positive frequency w, > 0, where o takes its maximum value, if it exists, is called the resonant frequency. 2 Let o = 0.8 Hz. Find the values of D for which the resonant frequency exists. (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (, ). Use the symbol co for 00 infinity and u for combining intervals, and the appropriate type of parenthesis " (", ") ", "[".") " depending on whether the interval is open or closed.)
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