Consider the system =7x+xy and =11y(y-x+5).Circle any equilibrium points. X=0, y
ID: 1719867 • Letter: C
Question
Consider the system =7x+xy and =11y(y-x+5).Circle any equilibrium points. X=0, y=5 x=2, y=-7 x=0, y=-5 x=11, y=-7 x=0, y=0 x=0, y=-7 Circle the letter of all the true statements about our damped harmonic oscillator model. We assume the damping force is proportional to the velocity, And in the same direction. We assume the spring force is proportional to the position, and in the same direction. When y=2, the spring is compressed. When y=0, the spring force is zero. They model can be a single first-order differential equation, or a system of two second-order differential equations. They model can be written in the form k +m +by=0, b>0, k>0. Friction is not factored into the damped harmonic oscillator model. A butter-knife is a convenient tool for stopping a damped harmonic oscillatorExplanation / Answer
Answer : An "equilibrium solution" is simply a constant solution and so its derivative is 0. At an equilibrium point we must have
dx/dt = 7x+xy = 0 implies x( 7 + y ) = 0
implies x = 0 or y = - 7
dy/dt = 11y( y - x + 5 ) = 0 implies y = 0 and y - x + 5 = 0
if x = 0 then y = - 5
3 )
a) Damping is in the opposite direction of velocity.
b) Spring force is in the opposite direction of postition
c) The amplitude is ambiguous
d) Traditionally this is true, as it makes the equation simplest. But it can be set up such that it is not true.
e) It is a 2nd order differential equation or a system of first order differential equation
f) Yes , The modal can be written in the given form
g) Friction is the dampening.
h) Yes , a butter - knife is a convenient tool stopping a damped harmonic oscillator.