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Figure 2 The massless rod in Fig. 2 has two masses on it, one mass mı...
5. Prove that: For two bodies with masses mı and m2 acting upon one another with...
5. Prove that: For two bodies with masses mı and m2 acting upon one another with equal and opposite (but not necessarily central) forces, the motion of one relative to the other takes place as if onefe.g. mı) were fixed and the other were replaced by a reduced mass equal to the mass product divided by the sum of the masses. 7n R r 0 2
4. Two objects of masses m/ and m2 are connected by a massless spring as shown...
4. Two objects of masses m/ and m2 are connected by a massless spring as shown in the figure below. The spring has a natural length of L and a stiffness of k. Owo a. If x is the extension of the spring by the horizontal motion of the masses, use Newton's second law to determine the equations of motion for each object. b. Combine these equations to show that the system oscillates at a frequency of - mįm2 w2...
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
The unforced, two-DOF figure shown has two masses. One is fixed at the end of a...
The unforced, two-DOF figure
shown has two masses. One is fixed at the end of a rigid, massless
rod, acting as pendulum which can swing about the point where it is
pinned. The system is at equilibrium when the pendulum hangs
straight down, with ф and x equal to 0. We may
assume that ф remains small.
In terms of the given mass, damping, and stiffness parameters
and the lengths shown:
a) Find the equations of motion of the two...
Problem 2 Two blocks (of masses m and m,) are connected by a massless string, as...
Problem 2 Two blocks (of masses m and m,) are connected by a massless string, as shown below. They are pulled up an incline of angle θ by a constant force applied to m2, which we'll call F., for convenience. (Note that, is the tension in the rope held by the woman and is directed parallel to the incline.) There is no friction between m, and the incline, but there is kinetic friction (of coefficient ) between m, and the...
Problem 3.35 (6 points) Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to a ...
part a and b only first paragraph already done (theta)
Problem 3.35 (6 points) Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to a wheel of mass 3 kgP and radius 0.05 m, as shown in Figure P3.34. A horizontal force f is applied to the wheel axle. Derive the equations of motion in terms of angular displacement θ of the rod and displacement-V,ofthe wheel center Assume the wheel does not slip. Linearize...
Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to...
Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to a wheel of mass 3 kg and radius 0.05 m, as shown in Figure P3.34. A horizontal force f is applied to the wheel axle. Derive the equations of motion in terms of angular displacement θ of the rod and displacement Xp of the wheel center Assume the wheel does not slip Linearize the resulting equations Extra credit (2 points each) a. If force...
Consider two masses: Mi=2.0 kg and M2 =1.5 kg. Mass Mı moves on a horizontal surface...
Consider two masses: Mi=2.0 kg and M2 =1.5 kg. Mass Mı moves on a horizontal surface where the coefficient of kinetic friction 4k = 0.40. Mass M2 is hanging freely. Two masses are connected by a strong cord of negligible mass that extends over a pulley. M = 2.0 kg 2 MK = 0.40 My = 1.5 kg a) Draw Free Body Diagrams for the two objects b) Write the equations for the two masses in the direction of motion...
2. Two point masses m and m2 are separated by a massless rod of length L....
2. Two point masses m and m2 are separated by a massless rod of length L. (a) Write an expression for the moment of inertia I about an axis perpendicular to the rod and passing through it a distance x from mass mi. (b) Calculate dl/dx and show that I is at a minimum when the axis passes through the center of mass of the system.
5. 10 points Two ideal massless springs with spring constant k are connected to two masses...
5. 10 points Two ideal massless springs with spring constant k are connected to two masses that hang vertically as shown in the figure. The top one has mass 3m and the bottom one has mass 2m. The system is only able to oscillate in the vertical direction. a) Determine the equations of motion. (4 pts) b) Find the frequencies of the normal modes of this system for small vertical dis- placements. (4 pts) c) Describe the relative motion and...
5. Prove that: For two bodies with masses mı and m2 acting upon one another with equal and opposite (but not necessarily central) forces, the motion of one relative to the other takes place as if onefe.g. mı) were fixed and the other were replaced by a reduced mass equal to the mass product divided by the sum of the masses. 7n R r 0 2
4. Two objects of masses m/ and m2 are connected by a massless spring as shown in the figure below. The spring has a natural length of L and a stiffness of k. Owo a. If x is the extension of the spring by the horizontal motion of the masses, use Newton's second law to determine the equations of motion for each object. b. Combine these equations to show that the system oscillates at a frequency of - mįm2 w2...
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
The unforced, two-DOF figure
shown has two masses. One is fixed at the end of a rigid, massless
rod, acting as pendulum which can swing about the point where it is
pinned. The system is at equilibrium when the pendulum hangs
straight down, with ф and x equal to 0. We may
assume that ф remains small.
In terms of the given mass, damping, and stiffness parameters
and the lengths shown:
a) Find the equations of motion of the two...
Problem 2 Two blocks (of masses m and m,) are connected by a massless string, as shown below. They are pulled up an incline of angle θ by a constant force applied to m2, which we'll call F., for convenience. (Note that, is the tension in the rope held by the woman and is directed parallel to the incline.) There is no friction between m, and the incline, but there is kinetic friction (of coefficient ) between m, and the...
part a and b only first paragraph already done (theta)
Problem 3.35 (6 points) Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to a wheel of mass 3 kgP and radius 0.05 m, as shown in Figure P3.34. A horizontal force f is applied to the wheel axle. Derive the equations of motion in terms of angular displacement θ of the rod and displacement-V,ofthe wheel center Assume the wheel does not slip. Linearize...
Figure P3.34 A slender rod 1.4 m long and of mass 20 kg is attached to a wheel of mass 3 kg and radius 0.05 m, as shown in Figure P3.34. A horizontal force f is applied to the wheel axle. Derive the equations of motion in terms of angular displacement θ of the rod and displacement Xp of the wheel center Assume the wheel does not slip Linearize the resulting equations Extra credit (2 points each) a. If force...
Consider two masses: Mi=2.0 kg and M2 =1.5 kg. Mass Mı moves on a horizontal surface where the coefficient of kinetic friction 4k = 0.40. Mass M2 is hanging freely. Two masses are connected by a strong cord of negligible mass that extends over a pulley. M = 2.0 kg 2 MK = 0.40 My = 1.5 kg a) Draw Free Body Diagrams for the two objects b) Write the equations for the two masses in the direction of motion...
2. Two point masses m and m2 are separated by a massless rod of length L. (a) Write an expression for the moment of inertia I about an axis perpendicular to the rod and passing through it a distance x from mass mi. (b) Calculate dl/dx and show that I is at a minimum when the axis passes through the center of mass of the system.
5. 10 points Two ideal massless springs with spring constant k are connected to two masses that hang vertically as shown in the figure. The top one has mass 3m and the bottom one has mass 2m. The system is only able to oscillate in the vertical direction. a) Determine the equations of motion. (4 pts) b) Find the frequencies of the normal modes of this system for small vertical dis- placements. (4 pts) c) Describe the relative motion and...
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