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a) Write down the Lagrangian L(x1, x2, 81, 82) for two particles of equal masses, m1...
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...
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...
Now, three masses m1=3.4kg, m2=10.2kg and m3=6.8kg x=14 hang from three identical springs in a motionless...
Now, three masses m1=3.4kg, m2=10.2kg and m3=6.8kg x=14 hang from three identical springs in a motionless elevator. Finally the elevator is moving downward with a velocity of v=-2.8m/s and also accelerating downward at an acceleration of a=-3.3m/s^2. The elevator is A. speeding up B. slowing down C. moving at a constant speed Rank the distances the springs are extended from their unstretched lengths: A. x1=x2=X3 B.X1>x2>x3 C. x1<x2<x3 what is the distance the Middle spring is extended from its unstretched...
Two equal masses, m, are joined by a massless string of length L that passes through...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
QUESTION 5 [25 marks] Two masses mi and m are joined by an inextensible string of...
QUESTION 5 [25 marks] Two masses mi and m are joined by an inextensible string of length I, as shown in Figure 2. The string passes over a massless pulley with frictionless bearings and radius R. The acceleration of gravity g points vertically downwards (a) 13 marks] Write down the Lagrangian, using the position of mass mi as the generalized coordinate m1 (b) 12 marks] Find the Lagrange equation of motion and solve it for 白m2 acceleration of mass mi...
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...
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...
Solve the following problems: Problem 1: masses&springs Two masses mand m2 connected by a spring of...
Solve the following problems:
Problem 1: masses&springs Two masses mand m2 connected by a spring of elastic constant k slide on a frictionless inclined plane under the effect of gravity. Let a be the angle between the the x axis and the inclined plane, r the distance between the two masses, l the position of the first mass with respect to the top of the plane (see figure). Considering the top of the plane to be the zero for potential...
A light, rigid rod of length l = 1.00 m joins two particles, with masses m1...
A
light, rigid rod of length l = 1.00 m joins two particles,
with masses m1 = 4.00 kg and
m2 = 3.00 kg, at its ends. The combination
rotates in the xy plane about a pivot through the center
of the rod (see figure below). Determine the angular momentum of
the system about the origin when the speed of each particle is
3.20 m/s.
magnitude
kg · m2/s
direction
chose the right
one ( +x , -x , +y...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
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...
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...
Two equal masses, m, are joined by a massless string of length L
that passes through a hole in a frictionless horizontal table.
First mass slides on table while the second hangs below the table
and moves up and down in a vertical line.
a.) Assuming the string remains taut, write down the Lagrangian
for the system in terms of the polar coordinates
of the mass on the table.
b.) Find the two Lagrangian equations of motion and interpret
the...
QUESTION 5 [25 marks] Two masses mi and m are joined by an inextensible string of length I, as shown in Figure 2. The string passes over a massless pulley with frictionless bearings and radius R. The acceleration of gravity g points vertically downwards (a) 13 marks] Write down the Lagrangian, using the position of mass mi as the generalized coordinate m1 (b) 12 marks] Find the Lagrange equation of motion and solve it for 白m2 acceleration of mass mi...
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...
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...
Solve the following problems:
Problem 1: masses&springs Two masses mand m2 connected by a spring of elastic constant k slide on a frictionless inclined plane under the effect of gravity. Let a be the angle between the the x axis and the inclined plane, r the distance between the two masses, l the position of the first mass with respect to the top of the plane (see figure). Considering the top of the plane to be the zero for potential...
A
light, rigid rod of length l = 1.00 m joins two particles,
with masses m1 = 4.00 kg and
m2 = 3.00 kg, at its ends. The combination
rotates in the xy plane about a pivot through the center
of the rod (see figure below). Determine the angular momentum of
the system about the origin when the speed of each particle is
3.20 m/s.
magnitude
kg · m2/s
direction
chose the right
one ( +x , -x , +y...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
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