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So rate of increasing amplitude is, 2/11.52=0.1736
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A damped vibrating system consists of a spring of stiffness k = 3,600 N/m and a...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg...
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping...
Question 3. A vibrating machine is fitted with a damped vibration absorber of the spring-mass type....
Question 3. A vibrating machine is fitted with a damped vibration absorber of the spring-mass type. The absorber has a mass of 5 kg, a damping ration of 0.6, and a damped natural frequency of 25Hz. Find the maximum dynamic force applied to the machine by the absorber when the machine is vibrating sinusoidally at 20HZ and with an amplitude of 1.5mm. machine: a = asin(wt) k C m y Hintl: Start with o, o/ N(1-5°) Hint2: The answer is...
QUESTION 6 130 MARKS For a vibrating system, the body mass is 10 kg, stiffness is 2.5 kN/m, and damping constant is 45...
QUESTION 6 130 MARKS For a vibrating system, the body mass is 10 kg, stiffness is 2.5 kN/m, and damping constant is 45 Ns/m. A harmonic force of amplitude 180 N and frequency 3.5 Hz acts on the mass. If the initial displacement and velocity of the mass are 15 mm and 5 m/s, compute the complete solution representing the motion of the mass. 45 (30 Marks)
QUESTION 6 130 MARKS For a vibrating system, the body mass is 10...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
A damped osillator has a mass (m = 2.00kg), a spring (k = 10.0N/m), and a...
A damped osillator has a mass (m = 2.00kg), a spring (k = 10.0N/m), and a damping coefficient b = 0.102kg/s. undamped angular frequency of the system is 2.24rad/s. If the initial amplitude is 0.250m, How many periods of motion are necessary for the amplitude to be reduced to 3/4 it initial value? is this system underdamped, critically damped, or overdamped
A damped harmonic oscillator consists of a block (m = 3.00 kg), a spring (k =...
A damped harmonic oscillator consists of a block (m = 3.00 kg), a spring (k = 11.1 N/m), and a damping force (F = -bv). Initially, it oscillates with an amplitude of 28.7 cm; because of the damping, the amplitude falls to 0.760 of the initial value at the completion of 6 oscillations. (a) What is the value of b? (Hint: Assume that b2 << km.) (b) How much energy has been lost during these 6 oscillations?
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if...
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
A system made up of a mass (m), attached to a spring of stiffness k [N/m]...
A system made up of a mass (m), attached to a spring of stiffness k [N/m] will oscillate to a specific amplitude (A) which will depend on an external force (F) and initial conditions. If all the variables involved are given in Table 1, formulate the necessary Pi groups to describe this behavior. Make sure you write the Pi groups using the parameters involved Variable Units A m m kg Parameter Amplitude Mass Spring constant External Force Frequency k N/m...
13. A damped mass-spring system with mass m, spring constant k, and damping constant b is driven by an external force with frequency w and amplitude Fo. 2662 where, wo is the (a) Show that the maximum oscillation amplitude occurs when w = natural frequency of the system. where, wd is the (b) Show that the maximum oscillation amplitude at that frequency is A = frequency of the undriven, damped system.
The system parameters of a freely-vibrating damped SDOF system are as follows: Mass, m= 100 kg Damping Factor, c = 200 kg/s Spring Stiffness, k = 3000 N/m Initial Position, x, = 1 m Initial Velocity, v,= 0 m/s a) Create a MATLAB code and using the specified system parameters compute (using the correct units) the system characteristics: 1) natural (circular) frequency on; 2) cyclic frequency fn; 3) cyclic period p; 4) damped natural (circular) frequency 0g, and 5) damping...
Question 3. A vibrating machine is fitted with a damped vibration absorber of the spring-mass type. The absorber has a mass of 5 kg, a damping ration of 0.6, and a damped natural frequency of 25Hz. Find the maximum dynamic force applied to the machine by the absorber when the machine is vibrating sinusoidally at 20HZ and with an amplitude of 1.5mm. machine: a = asin(wt) k C m y Hintl: Start with o, o/ N(1-5°) Hint2: The answer is...
QUESTION 6 130 MARKS For a vibrating system, the body mass is 10 kg, stiffness is 2.5 kN/m, and damping constant is 45 Ns/m. A harmonic force of amplitude 180 N and frequency 3.5 Hz acts on the mass. If the initial displacement and velocity of the mass are 15 mm and 5 m/s, compute the complete solution representing the motion of the mass. 45 (30 Marks)
QUESTION 6 130 MARKS For a vibrating system, the body mass is 10...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
2 with spring stiffness k 1000 N/m, Consider a mass-spring-damper system shown in Figure mass m = 10 kg, and damping constant c-150 N-s/m. If the initial displacement is xo-o and the initial velocity is 10 m/s (1) Find the damping ratio. (2) Is the system underdamped or overdamped? Why? (3) Calculate the damped natural frequency (4) Determine the free vibration response of the system.
QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if the spring stiffness is 3000 N/m and the damping coefficient c is set at 320 Ns/m. If a periodic 260 N force is applied to the mass at a frequency of 2 Hz, determine the amplitude of the forced vibration. Spring Viscous damper 35 kg Figure 4
A system made up of a mass (m), attached to a spring of stiffness k [N/m] will oscillate to a specific amplitude (A) which will depend on an external force (F) and initial conditions. If all the variables involved are given in Table 1, formulate the necessary Pi groups to describe this behavior. Make sure you write the Pi groups using the parameters involved Variable Units A m m kg Parameter Amplitude Mass Spring constant External Force Frequency k N/m...
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