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 displacementis written in the following form:
is written in the following form:
2) Deduce the second differential equation whose unknown is the
displacement 
3) Determine the free oscillations movement of each mass when by example, we move the mass m1 from its equilibrium position by abandoning it to itself without initial speed, the mass m2 being initially maintained at its position of static equilibrium without initial velocity (consider here: m1 = m2 = 1kg and k1 = k2 = k3 = 100 N / m).
Homework Answers
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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...
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...
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...
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...
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...
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 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)...
Show the movement of the masses with time by creating a MATLAB GUIDE file that takes...
Show the movement of the masses with time by creating a MATLAB
GUIDE file that takes the results of the Simulink analysis.
ki - 20 N/m; k2 = 12 N/m; m m = mot more = m + Mop ks = 7 N/m; c=2 N.s/m; mi - 20 kg; www Пw— m2 - 7 kg; 2. Simulink simout3 simout2 simout 1 1. Mathematical model m x2 + kı(X2 - u) + k_(x2-x2)+kz(x2 - X3)=0 m2ïz + k3(x3 - x2)=0 kz(x1...
If mass m1 is displaced 1 in. from its static equilibrium position and released, determine the...
If mass m1 is displaced 1 in. from its static equilibrium
position and released, determine the resulting displacements x1(t)
and x2(t) of the masses shown.
5. If mass m1 is displaced 1 in. from its static equilibrium position and released, determine the resulting displacements xi(t) and xz(t) of the masses shown.
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...
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...
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...
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...
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 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)...
Show the movement of the masses with time by creating a MATLAB
GUIDE file that takes the results of the Simulink analysis.
ki - 20 N/m; k2 = 12 N/m; m m = mot more = m + Mop ks = 7 N/m; c=2 N.s/m; mi - 20 kg; www Пw— m2 - 7 kg; 2. Simulink simout3 simout2 simout 1 1. Mathematical model m x2 + kı(X2 - u) + k_(x2-x2)+kz(x2 - X3)=0 m2ïz + k3(x3 - x2)=0 kz(x1...
If mass m1 is displaced 1 in. from its static equilibrium
position and released, determine the resulting displacements x1(t)
and x2(t) of the masses shown.
5. If mass m1 is displaced 1 in. from its static equilibrium position and released, determine the resulting displacements xi(t) and xz(t) of the masses shown.
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