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4. Determine the natural period t of horizontal vibrations of a simplified model of a single-...
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...
Model for Evaluation The model used for evaluation is the single degree of freedom lumped mass mo...
Model for Evaluation The model used for evaluation is the single degree of freedom lumped mass model defined by second order differential equation with constant coefficients. This model is shown in Figure 1. x(t)m m f(t) Figure 1 - Single Degree of Freedom Model The equation of motion describing this system can easily be shown to be md-x + cdx + kx = f(t) dt dt where m is the mass, c is the damping and k is the stiffness...
Question 2 A particle of mass m, is attached to a spring of natural length 2le...
Question 2 A particle of mass m, is attached to a spring of natural length 2le and stiffness 2k, and a second spring of stiffness k and natural length lo. It lies on a smooth horizontal table. and the two spring ends are a fixed distance 4lo apart, as shown in Figure Q2. The particle is released from rest at a distance 2lo from each end. Let x be the distance of the particle from A wwwwwwwwww Figure 02 (a)...
Determine the natural vibration period and damping ratio of the aluminum frame model from the acceleration...
Determine the natural vibration period and damping ratio of the aluminum frame model from the acceleration record of its free vibration shown in the figure bellow. Acceleration, g 0 1 2 3 5 6 7 8 4 Time, sec
A pipe carrying steam through a section of a factory vibrates violently when the driving pump hits a speed of 300 RPM. In an attempt to suppress the pipe vibrations completely, an absorber tuned to 3...
A pipe carrying steam through a section of a factory vibrates violently when the driving pump hits a speed of 300 RPM. In an attempt to suppress the pipe vibrations completely, an absorber tuned to 300 RPM is attached 4 The steam carrying pipe with the absorber in place can be modelled as shown in Figure Q4 below (a) Develop expressions for the amplitudes of the motion of the pipe and the (12) absorber masses as a function of the...
2. The electromechanical system shown in the figure below represents a simplified model of a capacitor...
2. The electromechanical system shown in the figure below represents a simplified model of a capacitor microphone. The system consists of a parallel plate capacitor connected into an electric circuit. Capacitor plate a is rigidly fixed to the microphone frame. Sound waves passing through the mouthpiece exert a force fs(t) on plate b, which has mass M and is connected to the frame by a set of springs and dampers The capacitance C is a function of the distance x...
Problem 4 (10 points) Astrom et a1 have presented a simplified second-order transfer function model for...
Problem 4 (10 points) Astrom et a1 have presented a simplified second-order transfer function model for bicycle dynamics as C1 Parameters defining the bicycle geometry. Schematic (a) top and (b) rear views of a bicycle The steer angle is δ and the roll angle is φ. The input is δ(t), the steering angle, and the output is Plt), the tilt angle (between the the bicycle longitudinal plane and the ground). In the model, parameter a is the horizontal distance from...
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 ...
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force F(t)-P, . cos(ω·) [lb] 0.5 in. 100 in. where the amplitude of harmonic force is Fo=50 lb and its angular frequency: ω-62832 radl s Model the system as a simple spring and mass system in the horizontal plane....
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 ...
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force Ft)-Fo.t) ibl. 0.5 in. Fio),x(t) 100 in. where the amplitude of harmonic force is F俨50 lh and its angular frequency: 62.832 radls Model the system as a simple spring and mass system in the horizontal plane. The mass...
General Information (Problems 2–4) The envelope of a four-story steel building (risk category II) is shown...
General Information (Problems 2–4) The envelope of a four-story steel building (risk category II) is shown below. Resistance to lateral loads (wind and earthquake) in the direction shown is provided by a steel braced frame on the interior of the building. The gravity load system, floor and roof diaphragms, and the lateral load system for the orthogonal direction are omitted from the figure. GRAVITY BF Roof 15 ft - - - - - - 15 ft WIND 3 15 ft...
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...
Model for Evaluation The model used for evaluation is the single degree of freedom lumped mass model defined by second order differential equation with constant coefficients. This model is shown in Figure 1. x(t)m m f(t) Figure 1 - Single Degree of Freedom Model The equation of motion describing this system can easily be shown to be md-x + cdx + kx = f(t) dt dt where m is the mass, c is the damping and k is the stiffness...
Question 2 A particle of mass m, is attached to a spring of natural length 2le and stiffness 2k, and a second spring of stiffness k and natural length lo. It lies on a smooth horizontal table. and the two spring ends are a fixed distance 4lo apart, as shown in Figure Q2. The particle is released from rest at a distance 2lo from each end. Let x be the distance of the particle from A wwwwwwwwww Figure 02 (a)...
Determine the natural vibration period and damping ratio of the aluminum frame model from the acceleration record of its free vibration shown in the figure bellow. Acceleration, g 0 1 2 3 5 6 7 8 4 Time, sec
A pipe carrying steam through a section of a factory vibrates violently when the driving pump hits a speed of 300 RPM. In an attempt to suppress the pipe vibrations completely, an absorber tuned to 300 RPM is attached 4 The steam carrying pipe with the absorber in place can be modelled as shown in Figure Q4 below (a) Develop expressions for the amplitudes of the motion of the pipe and the (12) absorber masses as a function of the...
2. The electromechanical system shown in the figure below represents a simplified model of a capacitor microphone. The system consists of a parallel plate capacitor connected into an electric circuit. Capacitor plate a is rigidly fixed to the microphone frame. Sound waves passing through the mouthpiece exert a force fs(t) on plate b, which has mass M and is connected to the frame by a set of springs and dampers The capacitance C is a function of the distance x...
Problem 4 (10 points) Astrom et a1 have presented a simplified second-order transfer function model for bicycle dynamics as C1 Parameters defining the bicycle geometry. Schematic (a) top and (b) rear views of a bicycle The steer angle is δ and the roll angle is φ. The input is δ(t), the steering angle, and the output is Plt), the tilt angle (between the the bicycle longitudinal plane and the ground). In the model, parameter a is the horizontal distance from...
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force F(t)-P, . cos(ω·) [lb] 0.5 in. 100 in. where the amplitude of harmonic force is Fo=50 lb and its angular frequency: ω-62832 radl s Model the system as a simple spring and mass system in the horizontal plane....
A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force Ft)-Fo.t) ibl. 0.5 in. Fio),x(t) 100 in. where the amplitude of harmonic force is F俨50 lh and its angular frequency: 62.832 radls Model the system as a simple spring and mass system in the horizontal plane. The mass...
General Information (Problems 2–4) The envelope of a four-story steel building (risk category II) is shown below. Resistance to lateral loads (wind and earthquake) in the direction shown is provided by a steel braced frame on the interior of the building. The gravity load system, floor and roof diaphragms, and the lateral load system for the orthogonal direction are omitted from the figure. GRAVITY BF Roof 15 ft - - - - - - 15 ft WIND 3 15 ft...
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