In the following Diagram the force (u) is applied to the mass
(M) and another mass (m) is connected to it.
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In the following Diagram the force (u) is applied to the mass
(M) and another mass...
2. In many mechanical positioning systems there is flexibility between one part of the system and...
2. In many mechanical positioning systems there is flexibility between one part of the system and another. The figure below depicts such a situation, where a force u(t) is applied to the mass M, and another mass m is connected to it. The coupling between the objects is often modeled by a spring constant k with a damping coefficient b, although the actual situation is usually much more complicated than this. y(t) m M ut) no friction no friction a)...
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1....
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...
Figure 4 shows a two-mass translational mechanical system. The applied force falt) acts on mass mi....
Figure 4 shows a two-mass translational mechanical system. The applied force falt) acts on mass mi. Displacements z1 and 22 are absolute positions of masses mi and m2, respectively, measured relative to fixed coordinates (the static equilibrium positions with fa(t) = 0). An oil film with viscous friction coefficient b separates masses mi and m2. Draw the free body diagram and derive the mathematical model of the vibration system using the diagram. falt) Oil film, friction coefficient b K m2...
16. A force of magnitude 25.0 N is applied to a box of mass m2 =...
16. A force of magnitude 25.0 N is applied to a box of mass m2 = 2.0 kg. The force is directed up a plane tilted at an angle of 60.0. The box is connected by a cord to another box of mass m1 = 2.5 kg. The floor and pulley are frictionless, the ramp has a coefficient of friction of μ,-0.15, and the masses of the pulley and cord are neglible. a. Draw the free-body diagrams for the two...
If the applied force P = 250 N, determine (a) the required minimum compression in the...
If the applied force P = 250 N, determine (a) the required
minimum compression in the spring so that the wedge will not move
to the right. Neglect the weight of A and B. The coefficient of
static friction for all contacting surfaces (i.e. between B &
A, and A & C) is ? = 0.35. Neglect friction at the rollers.
(b) Draw the free body diagram of object A. (Final Answer =
0.0183 m)
QUESTION ? 1 poi A child on a sled (total mass-35k) is pushed by another child...
QUESTION ? 1 poi A child on a sled (total mass-35k) is pushed by another child along a horizontal surface at a constant velocity. The pushing force has a magnitude 463 N which is applied at 8 = 26 90 angle as shown above. Frictional force is also present. Draw a free-body diagram for the child-sled system and determine the normal force in N with 3 significant figures Acceleration due to gravity - 9.30 m QUESTIONS A child on a...
A force of magnitude 12 N is applied to mass m2 1.4 kg. The force is...
A force of magnitude 12 N is applied to mass m2 1.4 kg. The force is directed up a plane tilted by θ 40°. The box is connected by a mass m-4.4 kg on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. (a) draw a free body diagram for each block in the system. (b) What is the tension in the cord? (c) what is the acceleration of the...
3. A bandage is made up of two identical patches of equal mass M, linked by...
3. A bandage is made up of two identical patches of equal mass M, linked by a vis- coelastic material, which we model with springs and dashpots. The bandage is fixed on the two ends. f(t) is the forced applied to the first mass, k is the spring constant and b is the damping coefficient. f(t) a) Draw the free-body diagram for both masses. (b) Describe the system by a set of ordinary differential equations. (c) Find the transfer function...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
2. In many mechanical positioning systems there is flexibility between one part of the system and another. The figure below depicts such a situation, where a force u(t) is applied to the mass M, and another mass m is connected to it. The coupling between the objects is often modeled by a spring constant k with a damping coefficient b, although the actual situation is usually much more complicated than this. y(t) m M ut) no friction no friction a)...
A quarter-car suspension model consisting of a spring and a damper is shown in Figure 1. An active suspension element produces an input force F. Draw a free-body diagram for the sprung mass m, and hence derive a differential equation relating the input force F to the sprung mass displacement x. (a) (5 marks) (b) Assuming a mass m-250kg, spring coefficient k 100Nm-1 and damping coefficient of c-50Nsm1, show that the transfer function from the input force F to the...
Figure 4 shows a two-mass translational mechanical system. The applied force falt) acts on mass mi. Displacements z1 and 22 are absolute positions of masses mi and m2, respectively, measured relative to fixed coordinates (the static equilibrium positions with fa(t) = 0). An oil film with viscous friction coefficient b separates masses mi and m2. Draw the free body diagram and derive the mathematical model of the vibration system using the diagram. falt) Oil film, friction coefficient b K m2...
16. A force of magnitude 25.0 N is applied to a box of mass m2 = 2.0 kg. The force is directed up a plane tilted at an angle of 60.0. The box is connected by a cord to another box of mass m1 = 2.5 kg. The floor and pulley are frictionless, the ramp has a coefficient of friction of μ,-0.15, and the masses of the pulley and cord are neglible. a. Draw the free-body diagrams for the two...
If the applied force P = 250 N, determine (a) the required
minimum compression in the spring so that the wedge will not move
to the right. Neglect the weight of A and B. The coefficient of
static friction for all contacting surfaces (i.e. between B &
A, and A & C) is ? = 0.35. Neglect friction at the rollers.
(b) Draw the free body diagram of object A. (Final Answer =
0.0183 m)
QUESTION ? 1 poi A child on a sled (total mass-35k) is pushed by another child along a horizontal surface at a constant velocity. The pushing force has a magnitude 463 N which is applied at 8 = 26 90 angle as shown above. Frictional force is also present. Draw a free-body diagram for the child-sled system and determine the normal force in N with 3 significant figures Acceleration due to gravity - 9.30 m QUESTIONS A child on a...
A force of magnitude 12 N is applied to mass m2 1.4 kg. The force is directed up a plane tilted by θ 40°. The box is connected by a mass m-4.4 kg on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. (a) draw a free body diagram for each block in the system. (b) What is the tension in the cord? (c) what is the acceleration of the...
3. A bandage is made up of two identical patches of equal mass M, linked by a vis- coelastic material, which we model with springs and dashpots. The bandage is fixed on the two ends. f(t) is the forced applied to the first mass, k is the spring constant and b is the damping coefficient. f(t) a) Draw the free-body diagram for both masses. (b) Describe the system by a set of ordinary differential equations. (c) Find the transfer function...
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
A single dof vibration system, modeled by a mass of 50 kg, damping coefficient of 300 Ns/m, and spring constant of 5000 N/m, is subjected to periodic displacement excitation u(t) as shown in the figure below. 1. Derive the equation of motion 2. Using Laplace transform, find characteristic equation. 3. Find the undamped and damped natural frequencies. 4. Find the damping ratio. 5. Find the transfer function of output x(t) to the periodic input u(t) using Laplace transform.
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