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 x2 (t)
3. using differentiel equations, Determine the free oscillation movement of each mass when, for example, we move the mass m1 away from its equilibrium position by abandoning it to itself without initial speed, the mass m2 being initially maintained at its static equilibrium position without initial speed (consider here: m1 = m2 = 1kg and k1 = k2 = k3 = 100 N / m).
Homework Answers
The differential equation describing the movement of the masses
can be found out by solving the Euler-Lagrangian equation.
Add Answer to:
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs...
We consider here, the two masses m1 and m2 connected this time by springs of stiffnesses...
We consider here, the two masses m1 and m2
connected this time by springs of stiffnesses k1,
k2 and k3 as shown in the figure below. We
denote by x1(t) and x2(t) the movement of
each of the 2 masses relative to its position of equilibrium
static.
1. Prove that the differential equation whose unknown is the
displacement x1(t) is written in the following form: (3
points)
2. Deduce the second differential equation whose unknown is the
displacement x2(t) (3...
We consider here, the two masses m1 and m2 connected this time by springs of stiffnesses...
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as shown in the figure
below. We denote x1 (t) and x2 (t) as the movement of each of the 2
masses relative to its position of equilibrium static.
1) Prove that the differential equation whose unknown is the displacement is written in the following form:
2) Deduce the second differential equation whose unknown is the
displacement
3) Determine the...
Here we consider the two masses m1 and m2 connected this time by springs of stiffnesses...
Here we consider the two masses m1 and m2 connected this time by
springs of stiffnesses k1, k2 and k3 as shown in the figure below.
The movement of each of the 2 masses relative to its position of
static equilibrium is designated by x1(t) and x2(t).
1. Demonstrate that the differential equation whose unknown is
the displacement x1(t) is written as follows:
2. Determine the second differential equation whose unknown is
the displacement x2(t).
3. Determine the free oscillatory...
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....
x2(t) m2 2 Two masses, m1 and m2, are connected with a spring, k. A force,...
x2(t) m2 2 Two masses, m1 and m2, are connected with a spring, k. A force, f (t), is applied on the first mass. Both masses experience viscous damping, c1 and c2, through the surface that they sit on. The equations of motion that describe the system dynamics are m2 (t)--CzX2 (t)-k(X2(t)-x,(t)) The initial conditions are: x1(0) - a x(0)b (0) = c Assuming zero initial conditions, rearrange the two equations of motion to find the response for X1(s) and...
DIFFÉRENTIEL EQUATIONS We consider 2 coupled harmonic oscillators, as shown in the diagram below. The mass...
DIFFÉRENTIEL EQUATIONS
We consider 2 coupled harmonic oscillators, as shown in the
diagram below.
The mass m1 is subjected to an external force F (t).
1. Construct the system of differential equations whose unknowns
are the displacements x1 (t) and x2 (t) of each of the 2 masses
(DIFFERENTIEL EQUATIONS).
2. Solve x1 (t) and x2 (t) in the case where m1 = 1kg; m2 = 2kg;
k = 1 N / m; F (t) = 0 and x1 (0)...
We consider 2 coupled harmonic oscillators, as shown in the diagram below The mass m1 is...
We consider 2 coupled harmonic oscillators, as shown in the
diagram below
The mass m1 is subjected to an external force F(t).
1) Construct the system of differential equations whose unknowns
are the displacements x1 (t) and x2 (t) of each of the 2
masses.
2) Solve x1 (t) and x2 (t) in the case where m1 = 1kg; m2 = 2kg;
k = 1 N / m; F (t) = 0 and x1 (0) = 0; ?1′ (0) =...
We consider 2 coupled harmonic oscillators, as shown in the diagram below. The mass m1 is...
We consider 2 coupled harmonic oscillators, as shown in the
diagram below.
The mass m1 is subjected to an external force F (t).
1. Construct the system of differential equations whose unknowns
are the displacements x1 (t) and x2 (t) of each of the 2 masses. (5
points).
2. Solve x1(t) and x2(t) in the case where
m1 = 1kg; m2 = 2kg; k = 1 N / m; F(t) = 0 and
x1(0) = 0; ?1′(0) = 0; x2(0)...
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 (-?
Classical Mechanics ! UD ︶ Two blocks of mass m1 and m2, respectively are connected by...
Classical Mechanics ! UD ︶ Two blocks of mass m1 and m2, respectively are connected by springs in the following way: mi m2 where on the very left there is a solid wall that does not move. As indicated in the picture, the displacement from the equilibrium position of blocks 1 and 2 is x1 and x2, respectively. Each spring exerts a force of F =-kx, where lxl is the displacement. What is the total force acting on each block...
We consider here, the two masses m1 and m2
connected this time by springs of stiffnesses k1,
k2 and k3 as shown in the figure below. We
denote by x1(t) and x2(t) the movement of
each of the 2 masses relative to its position of equilibrium
static.
1. Prove that the differential equation whose unknown is the
displacement x1(t) is written in the following form: (3
points)
2. Deduce the second differential equation whose unknown is the
displacement x2(t) (3...
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as shown in the figure
below. We denote x1 (t) and x2 (t) as the movement of each of the 2
masses relative to its position of equilibrium static.
1) Prove that the differential equation whose unknown is the displacement is written in the following form:
2) Deduce the second differential equation whose unknown is the
displacement
3) Determine the...
Here we consider the two masses m1 and m2 connected this time by
springs of stiffnesses k1, k2 and k3 as shown in the figure below.
The movement of each of the 2 masses relative to its position of
static equilibrium is designated by x1(t) and x2(t).
1. Demonstrate that the differential equation whose unknown is
the displacement x1(t) is written as follows:
2. Determine the second differential equation whose unknown is
the displacement x2(t).
3. Determine the free oscillatory...
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....
x2(t) m2 2 Two masses, m1 and m2, are connected with a spring, k. A force, f (t), is applied on the first mass. Both masses experience viscous damping, c1 and c2, through the surface that they sit on. The equations of motion that describe the system dynamics are m2 (t)--CzX2 (t)-k(X2(t)-x,(t)) The initial conditions are: x1(0) - a x(0)b (0) = c Assuming zero initial conditions, rearrange the two equations of motion to find the response for X1(s) and...
DIFFÉRENTIEL EQUATIONS
We consider 2 coupled harmonic oscillators, as shown in the
diagram below.
The mass m1 is subjected to an external force F (t).
1. Construct the system of differential equations whose unknowns
are the displacements x1 (t) and x2 (t) of each of the 2 masses
(DIFFERENTIEL EQUATIONS).
2. Solve x1 (t) and x2 (t) in the case where m1 = 1kg; m2 = 2kg;
k = 1 N / m; F (t) = 0 and x1 (0)...
We consider 2 coupled harmonic oscillators, as shown in the
diagram below
The mass m1 is subjected to an external force F(t).
1) Construct the system of differential equations whose unknowns
are the displacements x1 (t) and x2 (t) of each of the 2
masses.
2) Solve x1 (t) and x2 (t) in the case where m1 = 1kg; m2 = 2kg;
k = 1 N / m; F (t) = 0 and x1 (0) = 0; ?1′ (0) =...
We consider 2 coupled harmonic oscillators, as shown in the
diagram below.
The mass m1 is subjected to an external force F (t).
1. Construct the system of differential equations whose unknowns
are the displacements x1 (t) and x2 (t) of each of the 2 masses. (5
points).
2. Solve x1(t) and x2(t) in the case where
m1 = 1kg; m2 = 2kg; k = 1 N / m; F(t) = 0 and
x1(0) = 0; ?1′(0) = 0; x2(0)...
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 (-?
Classical Mechanics ! UD ︶ Two blocks of mass m1 and m2, respectively are connected by springs in the following way: mi m2 where on the very left there is a solid wall that does not move. As indicated in the picture, the displacement from the equilibrium position of blocks 1 and 2 is x1 and x2, respectively. Each spring exerts a force of F =-kx, where lxl is the displacement. What is the total force acting on each block...
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