Is it possible to force a system into the unstable equilibrium? Specifically in a system of...
Is it possible to force a system into the unstable equilibrium?
Specifically in a system of hysteresis, in the real world is it possible to force a system into an unstable equilibrium, or will it continually jump between stable points despite forcing the natural system?
Homework Answers
The body is said to be in equilibrium if the resultant of all
forces acting on it is zero. There are two major types of static
equilibrium, namely, translational equilibrium and rotational
equilibrium.
there are some condition for
equilibrium
Concurrent force system
ΣFx=0
ΣFy=0
Parallel Force System
ΣF=0
ΣMO=0
Non-Concurrent Non-Parallel Force System
ΣFx=0
ΣFy=0
ΣMO=0
now we can say that in a real life there is not possible that is force on system is in unequilibrium condition
if force is unstable then the energy of environment is unstable which is not possible
Add Answer to:
Is it possible to force a system into the unstable
equilibrium?
Specifically in a system of...
1. (20 points) Let (a) Determine and plot the equilibrium points and nullclines of the system....
1. (20 points) Let
(a) Determine and plot the equilibrium points and nullclines of
the system.
(b) Show the direction of the vector field between the
nullclines
(c) Sketch some solution curves starting near, but not on, the
equilibrium point(s).
(d) Label each equilibrium point as stable or unstable depending on
the behavior of the
solutions nearby, and describe the long-term behavior of all of the
solutions.
1. (25 pts) An autonomous differential equation has an unstable equilibrium solution at y = -1,...
1. (25 pts) An autonomous differential equation has an unstable equilibrium solution at y = -1, a semi-stable equilibrium solution at y = 0, and a stable equilibrium at y = 5/2. a. Sketch the slope field for the system. b. Propose a first order differential equation (use x as the independent variable) that meets the description above. c. What solution method(s) can be used to solve this system?
The force acting on a particle constrained to move in 1-dimension is given by: F= ax(b-...
The force acting on a particle constrained to move in 1-dimension is given by: F= ax(b- cx?) [a= 3.25, b=2.05, c=7.33] Find the three equilibrium points, and enter them left-to-right in order of ascending x-coordinate. Then, label each equilibrium point as "stable" or "unstable". Number Number Number Equilibrium Points: Stability: stable unstable
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit...
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
Consider a particle with a mass m subject to a force F(x) = ax - bx3...
Consider a particle with a mass m subject to a force F(x) = ax - bx3 where x is the displacement of the origin of the reference system and a and b are positive constants. a) Find an expression of the particle's total energy. Show that this total energy is constant. b) Find the equilibrium points and determine if they are stable or unstable.
Classify (if possible) each critical point of the given plane autonomous system as a stable node,...
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = xy - 3y - 4 y' = y2 - x2 Conclusion (x, y) =( stable spiral point (x, y) =( unstable spiral point
. (15 points) An unstable system can be stabilized by using negative feedback with a gain...
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
for the range of oso a 180, find the locations of equilibrium of the system and...
for the range of oso a 180, find the locations of equilibrium of the system and mention in whether the equilibrium is stable, Unstable neutral. each case Oy 1.58 fig. I: Two uniform rods of mass m and length, e attached to gears are 3 20
for the range of oso a 180, find the locations of equilibrium of the system and...
for the range of oso a 180, find the locations of equilibrium of the system and mention in whether the equilibrium is stable, Unstable neutral. each case Oy 1.58 fig. I: Two uniform rods of mass m and length, e attached to gears are 3 20
for the range of osoa 180 find the locations of equilibrium of the system and mention...
for the range of osoa 180 find the locations of equilibrium of the system and mention in whether the equilibrium is stable, neutral. each case Unstable 1.58, figol: Two uniform rods of mass m and length, e attached to gears are 34 20
1. (20 points) Let
(a) Determine and plot the equilibrium points and nullclines of
the system.
(b) Show the direction of the vector field between the
nullclines
(c) Sketch some solution curves starting near, but not on, the
equilibrium point(s).
(d) Label each equilibrium point as stable or unstable depending on
the behavior of the
solutions nearby, and describe the long-term behavior of all of the
solutions.
1. (25 pts) An autonomous differential equation has an unstable equilibrium solution at y = -1, a semi-stable equilibrium solution at y = 0, and a stable equilibrium at y = 5/2. a. Sketch the slope field for the system. b. Propose a first order differential equation (use x as the independent variable) that meets the description above. c. What solution method(s) can be used to solve this system?
The force acting on a particle constrained to move in 1-dimension is given by: F= ax(b- cx?) [a= 3.25, b=2.05, c=7.33] Find the three equilibrium points, and enter them left-to-right in order of ascending x-coordinate. Then, label each equilibrium point as "stable" or "unstable". Number Number Number Equilibrium Points: Stability: stable unstable
5. Consider the system: dz 4y 1 dy (a) Are these species predator-prey or competing? b) What type of growth does species z exhibit in absence of species y? What type of growth does species y exhibit in absence of species r? (c) Find all critical (equilibrium) points d) Using the Jacobian matrix, classify (if possible) each critical (equilibrium) point as a stable node, a stable spiral point, an unstable node, an unstable spiral point, or a saddle point. (e)...
Classify (if possible) each critical point of the given plane autonomous system as a stable node, a stable spiral point, an unstable spiral point, an unstable node, or a saddle point. (Order your answers from smallest to largest x, then from smallest to largest y.) x' = xy - 3y - 4 y' = y2 - x2 Conclusion (x, y) =( stable spiral point (x, y) =( unstable spiral point
. (15 points) An unstable system can be stabilized by using negative feedback with a gain K in the feedback loop. For instance, consider an unstable system with transfer function which has a pole in the right-hand s-plane, making the impulse response of the system h) grow as increases. Use negative feedback with a gain K> 0 in the feedback loop, and put H) in the forward loop. Draw a block diagram of the system. Obtain the transfer function Gus)...
for the range of oso a 180, find the locations of equilibrium of the system and mention in whether the equilibrium is stable, Unstable neutral. each case Oy 1.58 fig. I: Two uniform rods of mass m and length, e attached to gears are 3 20
for the range of oso a 180, find the locations of equilibrium of the system and mention in whether the equilibrium is stable, Unstable neutral. each case Oy 1.58 fig. I: Two uniform rods of mass m and length, e attached to gears are 3 20
for the range of osoa 180 find the locations of equilibrium of the system and mention in whether the equilibrium is stable, neutral. each case Unstable 1.58, figol: Two uniform rods of mass m and length, e attached to gears are 34 20
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