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. An airplane standing on a runway is shown in Figure Q4. The airplane mass is...
Consider the system shown in the figure below. The mass moment of inertia of the bar...
Consider the system shown in the figure below. The mass moment
of inertia of the bar about the point O is JO, and the torsional
stiffness of the spring attached to the pivot point is kt . Assume
that there is gravity loading. The centre of gravity of the bar is
midways, as shown in the figure.
Question 2 Consider the system shown in the figure below. The mass moment of inertia of the bar about the point O is...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the figure below. If the runway surface is described by y() = Ycoswt, determine the value of the damping coefficient c that gives an amplitude of vibration of the airplane of 1.0 mm. Assume m 153 rad/s. 1.8 mm, and w 2200 kg, k 4.9 MN/m, Y = x(e) Housing with strut and viscous damping Mass of aircraft y(e) Runway ww.
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two per...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
A door shown in the figure) undergoes rotational motions about the vertical axis. The governing equation...
A door shown in the figure) undergoes rotational motions about the vertical axis. The governing equation of rotational motion is given by Jyö + C70 + k 0 = 0 where Jo is the moment of inertia of the door, Ct is the rotational viscous damping and kt is the rotational stiffness of the door hinge. Assume that the door is 0.8 m wide (L = 0.8 m) and has a mass m of 15 kg. The moment of inertia...
Free body diagram: 24 0.5r 0.5r No slip (a) An ec centric disk is rotating on the ground as shown in the figure above. The disk has radius r. The distance between the center of mass of th...
Free body diagram: 24 0.5r 0.5r No slip (a) An ec centric disk is rotating on the ground as shown in the figure above. The disk has radius r. The distance between the center of mass of the disk (denoted as C) to its geometric center (denoted as O) is 1 r. The angle of rotation of the disk is θ and the displacement at point O is x. The disk has mass m. The moment of inertia with respect...
Could someone please help me with P8: "Compute the moment of inertia of the rod rotating...
Could someone please help me with P8: "Compute the moment of
inertia of the rod rotating around the pivot." and P10: "Write the
period of oscillation of the physical pendulum in terms of its
physical properties and compute its actual value."
Problem 3: Torque and Periodic Motion Consider a rigid uniform rod of length d2m and mass m-1kg pivoted at one end. The pendulum is initially displaced to one side by a small angle 8 2 and released from rest....
Solve a,b and c The vibratory movement of the engineering system shown in Figure 3 can...
Solve a,b and c
The vibratory movement of the engineering system shown in Figure 3 can be described by two generalised coordinates, x, a Cartesian coordinate, and 6, a polar coordinate systems. The mass m and its mass moment of inertia about an axis that goes through its centre of gravity G is J. When the system is slightly pushed down from the top comer at the right hand edge of mass m, the induced vibrational motion is found to...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spr...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
The figure shown below represents a simplified model of a jet engine mounted to a wing...
The figure shown below
represents a simplified model of a jet engine mounted to a wing
through a mechanism that acts as a spring of stiffness k and has a
mass ms. Assume the engine has a moment of inertia J and mass m and
that the rotation of the engine (i.e. the vectoring of the engine)
is related to the vertical displacement of the engine, x(t), by the
radius, ro (i.e. x=ro). Calculate the equation of motion, x(t) of...
Consider the system shown in the figure below. The mass moment
of inertia of the bar about the point O is JO, and the torsional
stiffness of the spring attached to the pivot point is kt . Assume
that there is gravity loading. The centre of gravity of the bar is
midways, as shown in the figure.
Question 2 Consider the system shown in the figure below. The mass moment of inertia of the bar about the point O is...
The landing gear of an airplane can be idealised as the spring-mass-damper system shown in the figure below. If the runway surface is described by y() = Ycoswt, determine the value of the damping coefficient c that gives an amplitude of vibration of the airplane of 1.0 mm. Assume m 153 rad/s. 1.8 mm, and w 2200 kg, k 4.9 MN/m, Y = x(e) Housing with strut and viscous damping Mass of aircraft y(e) Runway ww.
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
A door shown in the figure) undergoes rotational motions about the vertical axis. The governing equation of rotational motion is given by Jyö + C70 + k 0 = 0 where Jo is the moment of inertia of the door, Ct is the rotational viscous damping and kt is the rotational stiffness of the door hinge. Assume that the door is 0.8 m wide (L = 0.8 m) and has a mass m of 15 kg. The moment of inertia...
Free body diagram: 24 0.5r 0.5r No slip (a) An ec centric disk is rotating on the ground as shown in the figure above. The disk has radius r. The distance between the center of mass of the disk (denoted as C) to its geometric center (denoted as O) is 1 r. The angle of rotation of the disk is θ and the displacement at point O is x. The disk has mass m. The moment of inertia with respect...
Could someone please help me with P8: "Compute the moment of
inertia of the rod rotating around the pivot." and P10: "Write the
period of oscillation of the physical pendulum in terms of its
physical properties and compute its actual value."
Problem 3: Torque and Periodic Motion Consider a rigid uniform rod of length d2m and mass m-1kg pivoted at one end. The pendulum is initially displaced to one side by a small angle 8 2 and released from rest....
Solve a,b and c
The vibratory movement of the engineering system shown in Figure 3 can be described by two generalised coordinates, x, a Cartesian coordinate, and 6, a polar coordinate systems. The mass m and its mass moment of inertia about an axis that goes through its centre of gravity G is J. When the system is slightly pushed down from the top comer at the right hand edge of mass m, the induced vibrational motion is found to...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
The figure shown below
represents a simplified model of a jet engine mounted to a wing
through a mechanism that acts as a spring of stiffness k and has a
mass ms. Assume the engine has a moment of inertia J and mass m and
that the rotation of the engine (i.e. the vectoring of the engine)
is related to the vertical displacement of the engine, x(t), by the
radius, ro (i.e. x=ro). Calculate the equation of motion, x(t) of...
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