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A bead of mass M is able to move without friction along a stationary horizontal rod...
A bead of mass m slides without friction along a rod, one end of which is...
A bead of mass m slides without friction along a rod, one end of which is pivoted in such a way that the rod can be revolved about the z-axis at a constant angle a, as shown in Fig. 2. The rod is driven with constant angular velocity w about Oz. Use Lagrange method to derive the equation of motion for the bead. Use the distance of m from the origin as generalized coordinate and discuss the motion of the...
A plane pendulum of length L and mass m is suspended from a block of mass...
A plane pendulum of length L and mass m is suspended from a
block of mass M. The block moves without friction and is
constrained to move horizontally only (i.e. along the x axis). You
may assume all motion is confined to the xy plane. At t = 0, both
masses are at rest, the block is at
, and the pendulum has angular deflection
with respect to the y axis.
a) Using
and
as generalized coordinates, find the Lagrangian...
A bead of mass m slides without friction along a rotating wire in the shape of...
A bead of mass m slides without friction along a rotating wire in the shape of a parabola with zar2, as shown below. The wire is rotating around the z-axis with constant angular velocity w z=ar2 (a) (0.5 point) Determine the Lagrangian for the system in terms of the coordinate r b) (1 point) Apply the Lagrange Equations to obtain the equation of motion. You (c) (0.5 points) Suppose that the bead is moving in a perfect circle of radius...
please advice into missing information. A bead of mass m is constrained to slide without friction...
please advice into missing information.
A bead of mass m is constrained to slide without friction on a circular hoop of radius R. The hoop is oriented vertically and is attached to a motor that rotates it at a constant angular speed o, as shown in the attached figure. The bead experiences a constant gravitational force directed downward, given as mg. Answer the following questions: (a) Find the Lagrangian for this system using appropriate variables. (b) Find the effective potential....
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without...
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the...
3. A particle of mass is constrained to move without friction along the x-axis, subject to...
3. A particle of mass is constrained to move without friction along the x-axis, subject to a potential energy siven by Ue) Uo/ constants. Show that for small oscillations about x 0, the particle undergoes simple harmonic motion. What condition on x is required for the oscillations to be "small" (i.e. simple harmonic)? Find the period Tof the oscillations. - 1) where Uo and b are positive
1. A block of mass m moves without friction on a horizontal plane. The body is...
1. A block of mass m moves without friction on a horizontal plane. The body is connected to a massless string which slides without friction over a fixed pulley. A massless pulley is fastened at the other end of the string. Over the pulley, which can rotate without friction, hangs another string which has two bodies of masses 3m and m fastened to its two ends respectively. Their motions are supposed to be strictly vertical. The acceleration of gravity is...
A slender, uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and p...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
FIGURE P6.6 Problem 6.8 Refer to Figure P6.8. The mass m, translates without friction along the platform. The pendulum...
FIGURE P6.6 Problem 6.8 Refer to Figure P6.8. The mass m, translates without friction along the platform. The pendulum is attached to m, and is free to rotate. Obtain the equation of motion. mi m2
A bead of mass m slides without friction along a rod, one end of which is pivoted in such a way that the rod can be revolved about the z-axis at a constant angle a, as shown in Fig. 2. The rod is driven with constant angular velocity w about Oz. Use Lagrange method to derive the equation of motion for the bead. Use the distance of m from the origin as generalized coordinate and discuss the motion of the...
A plane pendulum of length L and mass m is suspended from a
block of mass M. The block moves without friction and is
constrained to move horizontally only (i.e. along the x axis). You
may assume all motion is confined to the xy plane. At t = 0, both
masses are at rest, the block is at
, and the pendulum has angular deflection
with respect to the y axis.
a) Using
and
as generalized coordinates, find the Lagrangian...
A bead of mass m slides without friction along a rotating wire in the shape of a parabola with zar2, as shown below. The wire is rotating around the z-axis with constant angular velocity w z=ar2 (a) (0.5 point) Determine the Lagrangian for the system in terms of the coordinate r b) (1 point) Apply the Lagrange Equations to obtain the equation of motion. You (c) (0.5 points) Suppose that the bead is moving in a perfect circle of radius...
please advice into missing information.
A bead of mass m is constrained to slide without friction on a circular hoop of radius R. The hoop is oriented vertically and is attached to a motor that rotates it at a constant angular speed o, as shown in the attached figure. The bead experiences a constant gravitational force directed downward, given as mg. Answer the following questions: (a) Find the Lagrangian for this system using appropriate variables. (b) Find the effective potential....
Q3-(25 pts) A small bead of mass m can move on a fixed horizontal wire without friction as in the figure. The bead is connected to an ideal spring of spring constant k, and the other end of the spring is connected to a fixed point at a perpendicular distance d from the wire. Unstretched length of the spring is very small, and can be taken to be zero. a) What is the period of oscillations of the bead around...
Problem 5 (15 points) A small bead can slide without friction on a circular hoop that is a vertical plane and has a radius of 0.100 m. The hoop rotates at a constant rate of 4.00 rev/sec (recall 1 rev = 2π rad) about a vertical diameter as shown in the figure below (a) Find the angle β at which the bead is in vertical equilibrium. (It has a radial acceleration toward the axis.) (b) Is it possible for the...
3. A particle of mass is constrained to move without friction along the x-axis, subject to a potential energy siven by Ue) Uo/ constants. Show that for small oscillations about x 0, the particle undergoes simple harmonic motion. What condition on x is required for the oscillations to be "small" (i.e. simple harmonic)? Find the period Tof the oscillations. - 1) where Uo and b are positive
1. A block of mass m moves without friction on a horizontal plane. The body is connected to a massless string which slides without friction over a fixed pulley. A massless pulley is fastened at the other end of the string. Over the pulley, which can rotate without friction, hangs another string which has two bodies of masses 3m and m fastened to its two ends respectively. Their motions are supposed to be strictly vertical. The acceleration of gravity is...
A slender, uniform metal rod of mass M and length l is pivoted
without friction about an axis through its midpoint and
perpendicular to the rod. A horizontal spring, assumed massless and
with force constant k, is attached to the lower end of the rod,
with the other end of the spring attached to a rigid support.
(Figure 1)
2. Find the torque τ due to the spring. Assume that θ is small
enough that the spring remains effectively horizontal...
FIGURE P6.6 Problem 6.8 Refer to Figure P6.8. The mass m, translates without friction along the platform. The pendulum is attached to m, and is free to rotate. Obtain the equation of motion. mi m2
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