Derive the frequency
A grinding machine is placed on a floor with a mass of 50 kg. Derive the frequency ratio when the displacement transmissibility reaches its maximum state.
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(20%) Problem 3 An industrial machine has a mass of 430 kg and operates at a speed of 1500 rpm. It appears it has a rot...
(20%) Problem 3 An industrial machine has a mass of 430 kg and operates at a speed of 1500 rpm. It appears it has a rotating unbalance of moe-0.8 kg.m. A structural engineer suggested that the maximum transmitted force to the floor is 10000 N. The only isolation available are units, each of 7 x 106 N/m stiffness and a 0.1 damping ratio. a. What is the maximum allowable transmissibility of the force due to the rotating mass to the...
The Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO) experiment was recently credited with confirming the existence...
The Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO) experiment was recently credited with confirming the existence of graviational waves for the first time. Key to its success was the development of a vibration isolation system to eliminate motion of lasers and mirrors. One requirement of the isolation system was to reduce seismic disturbances (base excitation) that oscillate at 0.16 Hz to produce system oscillations with a displacement transmissiblility is 1/10. The mass of the isolation mount is to be 100...
7 points| Consider a machine with rotating unbalance as described in Figure 1. At resonance, the ...
7 points| Consider a machine with rotating unbalance as described in Figure 1. At resonance, the maximum deflection is measured to be 0.1m. From manufacturing data, the out of balance mass, mo, is estimated to be 10% of the total mass m and the radius e is estimated to be 0.2m Guide Guide x(t) Machine of total mass mn Friction-free surface Rubber floor mounting modeled as a spring and a damper Figure 1: A model of rotation unbalance (a) Determine...
Please answer the following question in detail and show the steps used to do derive the...
Please answer the following question in detail and show the
steps used to do derive the correct answer. Please show all work
and circle final answer.
ll T-Mobile 21:04 Exit A uniform sheet of charge lies on a horizontal surface. A point charge of -8 micro-coulombs is located 0.13 meters below the sheet. At a point 0.31 meters above the sheet, directly above the charge, the total electric field from the sheet and the point charge is zero. Then, the...
Please Answer the following question in detail showing the step to derive the answer. Please show...
Please Answer the following question in detail showing the
step to derive the answer. Please show all work clearly and circle
final answer.
ll T-Mobile 18:35 Exit A uniform sheet of charge lies on a horizontal surface. A point charge of -8 micro-coulombs is located 0.18 meters below the sheet. At a point 0.40 meters above the sheet, directly above the charge, the total electric field from the sheet and the point charge is zero. Then, the point charge below...
A 15.5 kg mass vibrates in simple harmonic motion with a frequency of 17.73 Hz. It...
A 15.5 kg mass vibrates in simple harmonic motion with a frequency of 17.73 Hz. It has a maximum displacement from equilibrium of +13.2 cm at time, t = 0.00 s. The displacement from equilibrium of the mass at time, t = 1.25 s is cm.
A precision machine is placed on a work bench. The ground vibration transmitted by a nearby...
A precision machine is placed on a work bench. The ground vibration transmitted by a nearby internal combustion engine causes the base (bench) to vibrate at a frequency of 25 Hz with an amplitude of 0.6 cm. Design an isolation system to prevent ground motion to be transmitted to the precision machine, and at least 85% of vibration isolation must be achieved. If the machine has a mass of 48 kg, and the damper in the isolator has a damping...
Problem 3 A damped harmonic oscillator is described by the displacement as a function of time,...
Problem 3 A damped harmonic oscillator is described by the displacement as a function of time, An observer finds that every time the mass reaches its maximum (positive) displacement, that displacement is 10.0% smaller than the previous maximum positive displacement. Calculate the ratio of the period T of the oscillator with damping, to the period To of the same oscillator without damping.
In the lecture note, the resonance of a forced oscillation is defined as a state where...
In the lecture note, the resonance of a forced oscillation is defined as a state where the amplitude of displacement reaches maximum. Resonance can also be defined for the acceleration, where the acceleration’s amplitude reaches maximum. (a) Find the frequency of acceleration resonance. (b) Assume the damping is very small, i.e. ? ≪ ?0, find the approximate expression of the frequency in (a) [Hint: using Taylor series] and compare it with the frequency of displacement resonance.
The single degree of freedom model of a vehicle shown below will be used to obtain...
The single degree of freedom model of a vehicle shown below will
be used to obtain a first
approximation of the dynamic behavior of the entire vehicle. The
mass m of the vehicle is
1200 kg when fully loaded and 400 kg when empty. The spring
constant k is 400 kN/m and
the damping ratio ζf is 0.4 when the vehicle is fully
loaded. The vehicle is traveling at 100
km/h over a road whose surface has a sinusoidally varying...
(20%) Problem 3 An industrial machine has a mass of 430 kg and operates at a speed of 1500 rpm. It appears it has a rotating unbalance of moe-0.8 kg.m. A structural engineer suggested that the maximum transmitted force to the floor is 10000 N. The only isolation available are units, each of 7 x 106 N/m stiffness and a 0.1 damping ratio. a. What is the maximum allowable transmissibility of the force due to the rotating mass to the...
The Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO) experiment was recently credited with confirming the existence of graviational waves for the first time. Key to its success was the development of a vibration isolation system to eliminate motion of lasers and mirrors. One requirement of the isolation system was to reduce seismic disturbances (base excitation) that oscillate at 0.16 Hz to produce system oscillations with a displacement transmissiblility is 1/10. The mass of the isolation mount is to be 100...
7 points| Consider a machine with rotating unbalance as described in Figure 1. At resonance, the maximum deflection is measured to be 0.1m. From manufacturing data, the out of balance mass, mo, is estimated to be 10% of the total mass m and the radius e is estimated to be 0.2m Guide Guide x(t) Machine of total mass mn Friction-free surface Rubber floor mounting modeled as a spring and a damper Figure 1: A model of rotation unbalance (a) Determine...
Please answer the following question in detail and show the
steps used to do derive the correct answer. Please show all work
and circle final answer.
ll T-Mobile 21:04 Exit A uniform sheet of charge lies on a horizontal surface. A point charge of -8 micro-coulombs is located 0.13 meters below the sheet. At a point 0.31 meters above the sheet, directly above the charge, the total electric field from the sheet and the point charge is zero. Then, the...
Please Answer the following question in detail showing the
step to derive the answer. Please show all work clearly and circle
final answer.
ll T-Mobile 18:35 Exit A uniform sheet of charge lies on a horizontal surface. A point charge of -8 micro-coulombs is located 0.18 meters below the sheet. At a point 0.40 meters above the sheet, directly above the charge, the total electric field from the sheet and the point charge is zero. Then, the point charge below...
A precision machine is placed on a work bench. The ground vibration transmitted by a nearby internal combustion engine causes the base (bench) to vibrate at a frequency of 25 Hz with an amplitude of 0.6 cm. Design an isolation system to prevent ground motion to be transmitted to the precision machine, and at least 85% of vibration isolation must be achieved. If the machine has a mass of 48 kg, and the damper in the isolator has a damping...
Problem 3 A damped harmonic oscillator is described by the displacement as a function of time, An observer finds that every time the mass reaches its maximum (positive) displacement, that displacement is 10.0% smaller than the previous maximum positive displacement. Calculate the ratio of the period T of the oscillator with damping, to the period To of the same oscillator without damping.
The single degree of freedom model of a vehicle shown below will
be used to obtain a first
approximation of the dynamic behavior of the entire vehicle. The
mass m of the vehicle is
1200 kg when fully loaded and 400 kg when empty. The spring
constant k is 400 kN/m and
the damping ratio ζf is 0.4 when the vehicle is fully
loaded. The vehicle is traveling at 100
km/h over a road whose surface has a sinusoidally varying...
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