Let a particle of unit mass be subject to a force where x is its displacement...

Question

Question

Let a particle of unit mass be subject to a force 3х 1+ 2х where x is its displacement from the coordinate origin and the mass = 2 kg.

a) Derive an equation for $\dot{y}$ in terms of x.

b) Derive an equation for $\frac{dy}{dx}$ , and find the equation for the phase space trajectory, y(x)

I believe Y is the equation given in the beginning of the problem

Answer 1

Answer #1

32 ya MT + 2x3 net harcot 2(1+229/2 V 1+ 206 32 S 3 V[ +27 22 Y1+22 1+22) 3 301.422 (1722) + 1+22 3 (1+r) Now j = dy a dyan d

Answer 2

Similar Homework Help Questions

Analytical mechanics seventh edition p.141 3.24 let a particle of unit mass be subject to a force...

analytical mechanics seventh edition p.141 3.24 let a particle of unit mass be subject to a force x-x^3 where x is its displacement from the coordinate origin (a) Find the equilibrium points, and tell whether they are stable or unstable (b) Calculate the total energy of the particle, and show that it is a conserved quantity (c) Calculate the trajectories of the particle in phase space
A particle moves through an xyz coordinate system while a force acts on the particle. When...

A particle moves through an xyz coordinate system while a force acts on the particle. When the particle has the position vector r = (2.00 m) - (3.00 m) + (2.00 m) , the force is F = Fx + (7.00 N) - (6.00 N) , and the corresponding torque about the origin is T = (4.00 N·m) + (10.0 N·m) + (11.0 N·m) . Determine Fx. We were unable to transcribe this imageWe were unable to transcribe this imageWe...
Let X be a banach space such that X= C([a,b]) where - ab+ with the sup...

Let X be a banach space such that X= C([a,b]) where - ab+ with the sup norm. Let x and f X. Show that the non linear integral equation u(x) = (sin u(y) dy + f(x) ) has a solution u X. (the integral is from a to b). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...

A particle moving in the x-y plane is attracted toward the origin by force . Calculate...

A particle moving in the x-y plane is attracted toward the origin by force . Calculate work done when the particle moves from A to B and then C. Use the Cartesian variable method for this problem. We were unable to transcribe this imageB (2a a) A(0.a) C( 20)
DIFFERENTIAL EQUATION PROBLEM An object with a mass of 2 kg moves along the x-axis and...

DIFFERENTIAL EQUATION PROBLEM An object with a mass of 2 kg moves along the x-axis and we will assume that the positive direction of movement is to the right. Only one force (in N) is present and opposes the movement. Let be the speed of the object (in m / s) at time t. The object starts from the origin (x = 0) with an initial speed of 75 m / s. Suppose that the resistance force has a magnitude...
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.

a particle of mass m is given velocity on rough horizontal surface Coefficient of friction is...

a particle of mass m is given velocity on rough horizontal surface Coefficient of friction is there is also variable external force acts on particle given by F=kV where K is constant & V is instaneous velocity direction of force at any instant is perpendicular to velocity the particle moves in an instaneous circular path of variable radius then time taken by particle to stop is time taken to reduce the angle between acceleration and velocity from to is Total...
Verify that is a solution for the central force . Find a in terms of k, (the reduced mass), an...

Verify that is a solution for the central force . Find a in terms of k, (the reduced mass), and l (the angular momentum). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let Y = Xβ + ε be the linear model where X be an n ×...

Let Y = Xβ + ε be the linear model where X be an n × p matrix with orthonormal columns (columns of X are orthogonal to each other and each column has length 1) Let be the least-squares estimate of β, and let be the ridge regression estimate with tuning parameter λ. Prove that for each j, . Note: The ridge regression estimate is given by: The least squares estimate is given by: We were unable to transcribe this...

1) A particle with mass m moves under the influence of a potential field . The...

1) A particle with mass m moves under the influence of a potential field . The particle wave function is stated by: for where and are constants. (a) Show that is not time dependent. (b) Determine as the normalization constant. (c) Calculate the energy and momentum of the particle. (d) Show that V (x /km/2h+it/k/m Aar exp (ar, t) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...