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Concept explainers
Interpretation:
To analyze the nonlinear system graphically and to sketch the
Concept Introduction:
The given equation is
The point at which the velocity is zero can be obtained by graphing the function
Stable points are points at which the local flow is toward them. They represent stable equilibria at which small disturbances damp out in time away from it.
Unstable points are points at which the local flow is away from them. They represent unstable equilibria.
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Chapter 2 Solutions
Nonlinear Dynamics and Chaos
- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.arrow_forwardy = (4 + x)-¹/2, Find the Linearization L(x) = = a = 5 at x = a.arrow_forwardFind an equation of the parabola y = ax2 + bx + c that passes through (0, 1) and is tangent to the line y = x − 1 at (1, 0)arrow_forward
- help me pleasearrow_forwardFind the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) = √√3ti + e4j + 6e¯¹k at t = 0. (Use symbolic notation and fractions where needed. Give your answers in the form (*,*,*).) v(0) : = a(0) = (Use symbolic notation and fractions where needed. Give your answers in the form (*,*,*). Use t for the parameter that takes all real values.) l(t): =arrow_forwardDetermine an equation of the tangent line to y = (e3x - 2)4 at the point (0,1) then solve for y.arrow_forward
- Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xyarrow_forwardFind the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) = √3ti + e¹¹j + 6e¯¹k at t = 0. (Use symbolic notation and fractions where needed. Give your answers in the form (*,*,*).) v(0) = a(0) = (Use symbolic notation and fractions where needed. Give your answers in the form (*,*,*). Use t for the parameter that takes all real values.) 1(t)arrow_forwardFind a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) = ³√x, a = 125.2 Set the center of the linearization as x= L(x) = ₁arrow_forward
- A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also experiences a resistive force nv, where n is a constant, owing to its motion through the air. The equation of motion of the mass is therefore dv ' dt exp(-ßt)v³ – nv. Find an expression for the velocity v of the mass as a function of time, given that it has an initial velocity vo.arrow_forwardThe graph of 3 (x² + y²)² = 100 (x² - y²), shown in the figure, is a lemniscate of Bernoulli. Find the equation of the tangent line at the point (4,2). Carrow_forwardA body moving along the x axis starts at position x = 0 at t = 0, and moves with velocity v(t) = at³ + bt + c. Find: (1) its acceleration as a function of time, and (2) its position as a function of time. Acceleration: a(t) = Position: r(t)arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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