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Stability of equilibrium points Find the equilibrium solution of the following equations, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to indicate only whether solutions are increasing or decreasing on either side of the equilibrium solution.
20.
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Calculus: Early Transcendentals (3rd Edition)
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- Transient Orifice Flow: Water is discharged from a reservoir through a long pipe as shown. By neglecting the change in the level of the reservoir, the transient velocity of the water flowing from the pipe, vt), can be expressed as: - Reservoir v(t) V2gh = tanh V2gh) Pipe Where h is the height of the fluid in the 7- reservoir, L is the length of the pipe, g is the acceleration due to gravity, and t is the time elapsed from the beginning of the flow Transient Orifice Flow: Determine the helght of the fluid in the reservoir at time, t= 2.5 seconds, given that the velocity at the outfall, vt) = 3 m/s, the acceleration due to gravity, g = 9.81 m/s? and the length of the pipe to outfall, L= 1.5 meters. Reservoir v(t) V2gh = tanh 2L 2gh water Pipe Hint: Transform the equation to a function of form: fih) = 0 Solve MANUALLY using BISECTION AND REGULA-FALSI METHODS, starting at xn = 0.1, Kg =1, E = 0.001 and If(*new)l < Earrow_forwardHand written plzarrow_forwardThe motion of an oscillating weight suspended from a spring was measured by a motion detector. The data were collected, and the approximate maximum displacements from equilibrium (y = 3) are labeled in the figure. The distance y from the motion detector is measured in centimeters, and the time t is measured in seconds. (0.125, 3.32) 4 (a) Is y a function of t? O Yes ○ No (0.375, 2.68) 0.9 Explain. ○ For some value of t there is more than one value of y. ○ For some value of y there is more than one value of t. OFor each value of t there corresponds one and only one value of y. For each value of y there is some value of t. ◇ For each value of y there corresponds one and only one value of t. (b) Approximate the amplitude and period. amplitude period cm S (c) Find a model for the data. y = (d) Use a graphing utility to graph the model in part (c). Compare the result with the data in the figure.arrow_forward
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