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Question 6 Ci m, I k2 Figure Q6 A unform bar of mass m and length...
1. A suspension system shown in the figure is modified by adding two additional springs each with a spring constant of k, kN/m in addition to the other existing three springs with k 90 kN/m each....
1. A suspension system shown in the figure is modified by adding two additional springs each with a spring constant of k, kN/m in addition to the other existing three springs with k 90 kN/m each. The design also adds two additional dampers in addition to the two existing dampers each with the same viscous damping coefficient c (= 4000 Ns/m). The viscous damping ratiofor the underdamped system, 7 is 0.95. The mass of the system, m = 150 kg....
Figure 1 shows a system comprising a bar with mass m=12 kg and the length of...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
The figure above shows a thin, uniform bar of length D = 1.27 m and mass...
The figure above shows a thin, uniform bar of length D
= 1.27 m and mass M = 0.96 kg pivoted at the top. The rod,
which is initially at rest, is struck by a particle whose mass is
m = 0.30 kg at a point x = 0.80d below
the pivot. Assume that the particle sticks to the rod. If the
maximum angle between the rod and the vertical following the
collision is 60°, find the speed of the...
Question: A block with mass of m = 3.78 kg is attached to springs with spring...
Question: A block with mass of m = 3.78 kg is attached to springs with spring constants of ki = 18.1 N/m and k = 25.6 N/m, in different configurations shown in the figures below. Assume in all these cases that friction is negligible. Part 1) You will need to calculate the period of oscillations for each situation In this situation the mass is connected between the two springs which are each connected to opposite walls (Figure 1). What is...
A uniform rod of mass m-6 kg has length L = 60 cm . Instead of...
A uniform rod of mass m-6 kg has length L = 60 cm . Instead of pivoting it at its end, we pivoted it at L/3 from the end as shown in the figure, we now set the rod into small angle oscillations. What is the period of the oscillation given that the moment of inertia about the pivot point is ml2/9? L/3 Pivot L С.М. 2L/3
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg is connected with a spring with stiffness k = 2000N/m and a damper with damping ratio š = 0.3. The bar is rotating about a point that is 10cm from the left end. (1) Calculate the total kinetic energy and total potential energy. (2) Derive the equation of motion using energy based approach. (3) Determine the undamped natural frequency and damped natural frequency of...
1) A ball of mass, m = 2.50 kg, floats on a pool of fluid, L...
1) A ball of mass, m = 2.50 kg, floats on a pool of fluid, L at either end of the pool by springs, as shown in Fig.-1. The left spring has a spring constant, 1.00 m wide. It is attached to supports 1) a. 65.0N/m, and equilibrium length, L0.600m. The spring on the right has a spring constant, k2-75.0N/m, and equilibrium length, L2-0.800m. L-1.00 m e. ki LI Figure 1 -A ball of mass, m = 2.50 kg, floats...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to t...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to the bob is defined by er,ce where er is the unit vector orientecd away from the origin and e completes the direct orthonormal basis. The pendulum makes an angle 0(t) between the radial direction and the vertical direction e(t) The position vector beinge ind...
Xosin(ot) Shown in the figure below is a rigid pendulum bar of I= 1 m and...
Xosin(ot) Shown in the figure below is a rigid pendulum bar of I= 1 m and mass m, 1 kg attached to a roller, of mass m, = 0.2 kg, whose motion is described by X, sin(@t), Xo = 1 [m]. Model the pendulum bar as a uniform slender rod which has a moment of inertia with respect to its mass centre Ig given by m1/12. Use tangential-normal coordinate system to analyze the dynamics of the pendulum bar and use...
1. A suspension system shown in the figure is modified by adding two additional springs each with a spring constant of k, kN/m in addition to the other existing three springs with k 90 kN/m each. The design also adds two additional dampers in addition to the two existing dampers each with the same viscous damping coefficient c (= 4000 Ns/m). The viscous damping ratiofor the underdamped system, 7 is 0.95. The mass of the system, m = 150 kg....
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
The figure above shows a thin, uniform bar of length D
= 1.27 m and mass M = 0.96 kg pivoted at the top. The rod,
which is initially at rest, is struck by a particle whose mass is
m = 0.30 kg at a point x = 0.80d below
the pivot. Assume that the particle sticks to the rod. If the
maximum angle between the rod and the vertical following the
collision is 60°, find the speed of the...
Question: A block with mass of m = 3.78 kg is attached to springs with spring constants of ki = 18.1 N/m and k = 25.6 N/m, in different configurations shown in the figures below. Assume in all these cases that friction is negligible. Part 1) You will need to calculate the period of oscillations for each situation In this situation the mass is connected between the two springs which are each connected to opposite walls (Figure 1). What is...
A uniform rod of mass m-6 kg has length L = 60 cm . Instead of pivoting it at its end, we pivoted it at L/3 from the end as shown in the figure, we now set the rod into small angle oscillations. What is the period of the oscillation given that the moment of inertia about the pivot point is ml2/9? L/3 Pivot L С.М. 2L/3
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg is connected with a spring with stiffness k = 2000N/m and a damper with damping ratio š = 0.3. The bar is rotating about a point that is 10cm from the left end. (1) Calculate the total kinetic energy and total potential energy. (2) Derive the equation of motion using energy based approach. (3) Determine the undamped natural frequency and damped natural frequency of...
1) A ball of mass, m = 2.50 kg, floats on a pool of fluid, L at either end of the pool by springs, as shown in Fig.-1. The left spring has a spring constant, 1.00 m wide. It is attached to supports 1) a. 65.0N/m, and equilibrium length, L0.600m. The spring on the right has a spring constant, k2-75.0N/m, and equilibrium length, L2-0.800m. L-1.00 m e. ki LI Figure 1 -A ball of mass, m = 2.50 kg, floats...
1) Consider a pendulum of constant length L to which a bob of mass m is attached. The Q6. pendulum moves only in a two-dimensional plane (see figure below). The polar frame of reference attached to the bob is defined by er,ce where er is the unit vector orientecd away from the origin and e completes the direct orthonormal basis. The pendulum makes an angle 0(t) between the radial direction and the vertical direction e(t) The position vector beinge ind...
Xosin(ot) Shown in the figure below is a rigid pendulum bar of I= 1 m and mass m, 1 kg attached to a roller, of mass m, = 0.2 kg, whose motion is described by X, sin(@t), Xo = 1 [m]. Model the pendulum bar as a uniform slender rod which has a moment of inertia with respect to its mass centre Ig given by m1/12. Use tangential-normal coordinate system to analyze the dynamics of the pendulum bar and use...
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