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.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Nonlinear Dynamics and Chaos
- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.arrow_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 an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xyarrow_forward
- Find 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_forwardA 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_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
- Determine an equation of the tangent line to y = (e3x - 2)4 at the point (0,1) then solve for y.arrow_forward(3) Suppose that the position function of a particle moving on a coordinate line is given by s(t) = ³-2t² + 3t - 7 in meters, where t is in seconds. (a) Find the velocity and acceleration functions; (b) Analyze the direction of the motion that shows when the particle is stopped, when it is moving forward and/or backward; (c) Analyze the change of speed that shows when it is speeding up and/or slowing down; (d) Find the total distance traveled by the particle from time t = 0 to t = 6 seconds.arrow_forwardA projectile is fired straight up from a platform 10ft above the ground, with an initial velocity of 160 ft/sec. Assume that the only force affecting the motion of the projectile during its flight is from gravity, which produces a downward acceleration of 32 ft/sec?. What is the equation for the height of the projectile above the ground as a function of time t if t = 0 when the projectile is fired? s = -16t2 + 80t + 10 s = 16t2 – 160t + 10 - O D A s = -16t2 – 160t + 10 s = -16t2 + 160t + 10 Barrow_forward
- find the homogenous linear equation of the function y = x2 sinx+ e5xarrow_forwardA particle's position with respect to time as it moves along a coordinate axis is given by the function p(t) = t³ + 3t² + 3t + 1. What is the particle's acceleration at time t = -3? Do not include "a(-3) =" in your answer.arrow_forwardy = (4 + x)-¹/2, Find the Linearization L(x) = = a = 5 at x = a.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,