Homework Answers
Add Answer to:
Consider the mass-spring system given below. Suppose that the upper weight is pulled down one unit and the lower weight is raised one unit, then both weights are released from rest simultaneously...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants k1, k2 and k3, respectively. x2=0 Il k, Let xi and x2 represent The motion of the equations: displacements of masses mi and m2 from their equilibrium positions . coupled system is represented by the system of second-order differential d2x dt2 d2x2 Using Laplace transform to solve the system when k1 1 and x1(0) = 0, xi (0)--1 , x2(0) = 0, x(0)-1....
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
Differentiel equations We consider here, the two masses m1 and m2 connected this time by springs...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Consider a mass-spring-damper system whose motion is described by the following system of differe...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
Consider a system of two toy rail cars (i.e.. frictionless masses)- Suppose that car 1 has...
Consider a system of two toy rail cars (i.e.. frictionless masses)- Suppose that car 1 has mass 6 kg and is traveling at 3 m/s toward the other car- Suppose car 2 has mass 3 kg and is moving toward the other car at 9 m/s. There is a bumper on the second rail car that engages at the moment the cars hit and does not let go (it connects the two cars). The bumper acts as a spring with...
4. Two masses mi and m2 are connected to three springs of negligible mass having spring constants k1, k2 and k3, respectively. x2=0 Il k, Let xi and x2 represent The motion of the equations: displacements of masses mi and m2 from their equilibrium positions . coupled system is represented by the system of second-order differential d2x dt2 d2x2 Using Laplace transform to solve the system when k1 1 and x1(0) = 0, xi (0)--1 , x2(0) = 0, x(0)-1....
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
6.(16) Consider the spring-mass system shown, consisting of two unit masses m, and my suspended from springs with constants k, and ky, respectively. Assuming that there is no damping in the system, the displacement y(t) of the bottom mass m, from its equilibrium positions satisfies the 4-order equation (4) y2 + k + k)y + k_k2yz = e-2, where f(t) = e-2 is an outside force driving the motion of m. If a 24 N weight would stretch the top...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Consider a mass-spring-damper system whose motion is described by the following system of differentiat equations [c1(f-k)+k,(f-х)-c2(x-9), f=f(t), y:' y(t) with x=x( t), where the function fit) is the input displacement function (known), while xit) and yt) are the two generalized coordinates (both unknown) of the mass-spring-damper systenm. 1. Identify the type of equations (e.g. H/NH, ODE/PDE, L/NL, order, type of coefficients, etc.J. 2. Express this system of differential equations in matrix form, assume f 0 and then determine its general...
1. Solve the initial value problem for a damped mass-spring system acted upon by a sinusoidal force for some time interval f(t) = {10 sin 2t 0 0<t< y(0) 1, y'(0) -5 y"2y' 2y f(t), Tt zusor= 2. Consider two masses and three springs without no external force. The resulting force balance can be expressed as two second order ODES shown as below. mx=-(k k2)x1+ kzx2 m2x2 (k2k3)x2 + k2x1 15 If m 2,m2 ki = 1,k2 = 3, k3...
Consider a system of two toy rail cars (i.e.. frictionless masses)- Suppose that car 1 has mass 6 kg and is traveling at 3 m/s toward the other car- Suppose car 2 has mass 3 kg and is moving toward the other car at 9 m/s. There is a bumper on the second rail car that engages at the moment the cars hit and does not let go (it connects the two cars). The bumper acts as a spring with...
Most questions answered within 3 hours.
-
convert grams into vloume with the density of water being at
.997514 g/cm^3 at 23.1 Celsuis...
asked 2 hours ago -
Foreman company obtained a $20,000, 6% loan on May 1, 2018.
Principal and interest will be...
asked 2 hours ago -
5. Problem 11.05 (Discounted Payback)
eBook
Project L costs $60,000, its expected cash inflows are $14,000
per...
asked 2 hours ago -
1. Which of the following is true about politics and health
organizations?
A. Health organizations are...
asked 2 hours ago -
A space vehicle is coasting at a constant velocity of 18.1 m/s
in the +y direction...
asked 3 hours ago -
5) Use the following balanced equation to answer questions
(a)-(i).
3 Cu(s) + 8 HNO3(aq) →...
asked 3 hours ago -
A three-year maturity bond with a 12% annual coupon rate is
currently traded at par $1000...
asked 3 hours ago -
1.
What is the minimum volume to use in the Spec 20 cuvette in order
to...
asked 4 hours ago -
A builder wants to install wall-to-wall carpeting in a living
room of length 8.87 m and...
asked 4 hours ago -
Organizational change can produce anxiety in those affected by
the change. In what ways can change...
asked 4 hours ago -
Ozone in the atmosphere may react with nitric oxide.
From the following data, calculate the DG...
asked 4 hours ago -
Steven Long, a bond analyst, is analyzing a convertible bond.
The characteristics of the bond are...
asked 4 hours ago