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1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the ma...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with dam...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with damping constant gy 2 connected (1) Find the total kinetic energy and total pot of the ystem,e total kinetic edamping constonnected with a spring with system. (2) Derive the equation of motion using e (3) Determine the undamped natural fir 4) Calculate the damping ratio of the sy nergy metho frequency of the system. Gven
L. 2 uestion 3...
A mass Mis supported on a firm base by a spring of stiffness k and a...
A mass Mis supported on a firm base by a spring of stiffness k and a damper with damping constant c. A mass m falls on the larger mass M from a height h and sticks to the latter without rebounding on impact. Find the equation governing the motion of the two masses after impact and determine their maximum displacement with reference to the position at impact. The following data are given: M-20 kg, m = 5 kg, k =...
A ball of mass M is attached to one end of a spring of stiffness k...
A ball of mass M is attached to one end of a spring of
stiffness k and relaxed length
L0. The other end of the spring
is attached to the ceiling. When the ball hangs at rest in
equilibrium at the end of the spring it is located at the origin of
the coordinate system shown and the spring’s length is
Leq.
a. The figure shows the ball at position . What are the components of the
vector Li that...
. The system shown below consists of a homogeneous rigid rod with mass m, length l,...
. The system shown below consists of a homogeneous rigid rod with mass m, length l, and mass center of gravity G where the mass moment of inertia of the rod about G is given by: Translational spring with stiffness k supports the rod at point B, and rotational damper c, İs connected to the rod at its pivot point A as shown.ft) is an external force applied to the rod. Derive the equation of motion of the single degree...
A mass of 50kg is hung from a spring of stiffness ?=?.?×105 (?/? ) and damper...
A mass of 50kg is hung from a spring of stiffness
?=?.?×105 (?/? ) and damper ?=100 ?.?/? , which is
attached to two aluminum beams with ?=71×109 (Pa),
moment of inertia ?=?.?×10−? (??), and length
of 255 (mm ). The beam is supported at its free end.
Determine:
(a) Equivalent stiffness and equation of motion of the
system.
(b) Damped natural frequency of the system (??) in
(Hz).
(c) Free vibration response of the system in time domain,?(?), when...
2) A particle of mass m, is attached to a massless rod of length L which...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
Example 24 A beam of length L and mass m, is pivoted at one end and...
Example 24 A beam of length L and mass m, is pivoted at one end and suspended from a spring of stiffness k distance L from the pivot. A dashpot is also positioned a distance R from the pivot. Show how the equation of motion below can be derived. de 3cR2 de dt 3kLi 0 = 0 mL2 mL dt where x is the displacement at the free end, and c is the damping coefficient (Ns/m)
Example 24 A beam...
1- Below figure a rod of AB by the length of 6.0 m and mass of...
1- Below figure a rod of AB by the length of 6.0 m and mass of 20.0 kg is hinged at one end and the other end is attached to a cord and cord to the wall. A mass of 60.0 kg is at 2.0 meter from the hinge and another mass with 80 kg is at 5.0 meter from hinge. At this situation find amount of tension in cord and exerted force from wall on the hinge. string 50...
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod...
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod is also pinned to a roller and held in place by two elastic springs with constants k .
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid...
please help for a-d. 1. Consider a beam of length L that is hinged at one...
please help for a-d.
1. Consider a beam of length L that is hinged at one end and supported by a cord at the other as shown in the figure. Suppose a mass M is hung at a distance of d from the hinge and that the supporting cord makes an angle of q 30 with the horizontal. Attached to the other end of the cord is a mass m. Take the mass of the beam m, to be equal...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with damping constant gy 2 connected (1) Find the total kinetic energy and total pot of the ystem,e total kinetic edamping constonnected with a spring with system. (2) Derive the equation of motion using e (3) Determine the undamped natural fir 4) Calculate the damping ratio of the sy nergy metho frequency of the system. Gven
L. 2 uestion 3...
A mass Mis supported on a firm base by a spring of stiffness k and a damper with damping constant c. A mass m falls on the larger mass M from a height h and sticks to the latter without rebounding on impact. Find the equation governing the motion of the two masses after impact and determine their maximum displacement with reference to the position at impact. The following data are given: M-20 kg, m = 5 kg, k =...
A ball of mass M is attached to one end of a spring of
stiffness k and relaxed length
L0. The other end of the spring
is attached to the ceiling. When the ball hangs at rest in
equilibrium at the end of the spring it is located at the origin of
the coordinate system shown and the spring’s length is
Leq.
a. The figure shows the ball at position . What are the components of the
vector Li that...
. The system shown below consists of a homogeneous rigid rod with mass m, length l, and mass center of gravity G where the mass moment of inertia of the rod about G is given by: Translational spring with stiffness k supports the rod at point B, and rotational damper c, İs connected to the rod at its pivot point A as shown.ft) is an external force applied to the rod. Derive the equation of motion of the single degree...
A mass of 50kg is hung from a spring of stiffness
?=?.?×105 (?/? ) and damper ?=100 ?.?/? , which is
attached to two aluminum beams with ?=71×109 (Pa),
moment of inertia ?=?.?×10−? (??), and length
of 255 (mm ). The beam is supported at its free end.
Determine:
(a) Equivalent stiffness and equation of motion of the
system.
(b) Damped natural frequency of the system (??) in
(Hz).
(c) Free vibration response of the system in time domain,?(?), when...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
Example 24 A beam of length L and mass m, is pivoted at one end and suspended from a spring of stiffness k distance L from the pivot. A dashpot is also positioned a distance R from the pivot. Show how the equation of motion below can be derived. de 3cR2 de dt 3kLi 0 = 0 mL2 mL dt where x is the displacement at the free end, and c is the damping coefficient (Ns/m)
Example 24 A beam...
1- Below figure a rod of AB by the length of 6.0 m and mass of 20.0 kg is hinged at one end and the other end is attached to a cord and cord to the wall. A mass of 60.0 kg is at 2.0 meter from the hinge and another mass with 80 kg is at 5.0 meter from hinge. At this situation find amount of tension in cord and exerted force from wall on the hinge. string 50...
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid rod of length is supported as a pendulum at end A, and has a mass m. The rod is also pinned to a roller and held in place by two elastic springs with constants k .
Problen /) Derive equations of motion of the system shown below in x and 0 by using Lagrange's method. The thin rigid...
please help for a-d.
1. Consider a beam of length L that is hinged at one end and supported by a cord at the other as shown in the figure. Suppose a mass M is hung at a distance of d from the hinge and that the supporting cord makes an angle of q 30 with the horizontal. Attached to the other end of the cord is a mass m. Take the mass of the beam m, to be equal...
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