Solution Found!
Figure P9.3 is a representation of the effects of the tide
Chapter , Problem 9.3(choose chapter or problem)
Figure P9.3 is a representation of the effects of the tide on a small body of water connected to the ocean by a channel. Assume that the ocean height \(h_{i}\) varies sinusoidally with a period of 12 hr with an amplitude of 3 ft about a mean height of 10 ft. If the observed amplitude of variation of \(\hat{h}\) is 2 ft, determine the time constant of the system and the time lag between a peak in \(h_{i}\) and a peak in \(\hat{h}\).
Questions & Answers
QUESTION:
Figure P9.3 is a representation of the effects of the tide on a small body of water connected to the ocean by a channel. Assume that the ocean height \(h_{i}\) varies sinusoidally with a period of 12 hr with an amplitude of 3 ft about a mean height of 10 ft. If the observed amplitude of variation of \(\hat{h}\) is 2 ft, determine the time constant of the system and the time lag between a peak in \(h_{i}\) and a peak in \(\hat{h}\).
Step 1 of 4
The following are given by the question:
The mean height of ocean, \(h_{i}=10 \mathrm{ft}\)
The amplitude, \(A=3 \mathrm{ft}\)
The variation in amplitude is \(2 \mathrm{ft}\)
The height of the ocean varies sinusoidally with a \(12 \mathrm{hr}\) time period.
The input expression,
\(\begin{array}{l} h_{i}(t)=h_{i}+A \sin \left(\frac{2 \pi}{12} t\right) \\ h_{i}(t)=10+3 \sin \left(\frac{2 \pi}{12} t+\phi\right) \end{array}\)
The steady state response expression,
\(h(t)=10+2 \sin \left(\frac{2 \pi}{12} t+\phi\right)\)