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QUESTION 4 (140 marks) Determine the damped frequency of the spring-mass system schematically illustrated below if...
A mass of 10 kg is suspended by a spring having a stiffness of 10000o N/m....
A mass of 10 kg is suspended by a spring having a stiffness of 10000o N/m. The viscous damping causes the amplitude to decrease to one-tenth of the initial value in four complete oscillations. If a periodic force of 150 cos 50t is applied to the mass in vertical direction, (a) Find the amplitude of the forced vibration (b) What is its amplitude at resonance? (c) Comment on the results obtained in part (a) and (b) (15 markah/marks)
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
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.
Can I get help with this 2. (20 points) The damped single degree-of-freedom mass-spring system shown...
Can
I get help with this
2. (20 points) The damped single degree-of-freedom mass-spring system shown below has a mass m- 20 kg and a spring stiffness coefficient k 2400 N/m. a) Determine the damping coefficient of the system, if it is given that the mass exhibits a response with an amplitude of 0.02 m when the support is harmonically excited at the natural frequency of the system with an amplitude Yo-0.007 m b) Determine the amplitude of the dynamic...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
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 damped system consists of a mass (m = 30kg) supported on a spring and a...
A damped system consists of a mass (m = 30kg) supported on a spring and a damper in parallel. In an experiment, the period of vibration of this system was measured to be 0.5 seconds, and the ratio of maximum displacement between two successive cycles was determined from the experimental data to be 20. Determine: a. The logarithmic decrement. [2] Q4a. Answer: b. The damping ratio, commenting if this is over-damped, critically damped, or under-damped. [4] Q4b. Answer: c. The...
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...
Consider a single degree of freedom (SDOF) with mass-spring-damper system
Consider a single degree of freedom (SDOF) with mass-spring-damper system subjected to harmonic excitation having the following characteristics: Mass, m = 850 kg; stiffness, k = 80 kN/m; damping constant, c = 2000 N.s/m, forcing function amplitude, f0 = 5 N; forcing frequency, ωt = 30 rad/s. (a) Calculate the steady-state response of the system and state whether the system is underdamped, critically damped, or overdamped. (b) What happen to the steady-state response when the damping is increased to 18000 N.s/m? (Hint: Determine...
ineers can determine properties of a structure that is modeled as damped spring oscillator-such as a...
ineers can determine properties of a structure that is modeled as damped spring oscillator-such as a bridge-by applying a driving force to it. A weakly damped spring oscillator of mass 0.242 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 34.0 Hz. Find the value of the spring constant Number N/ m The amplitude of the driving force is 0.471 N and the amplitude of the oscillator's steady-state motion in response to this driving force is...
A mass of 10 kg is suspended by a spring having a stiffness of 10000o N/m. The viscous damping causes the amplitude to decrease to one-tenth of the initial value in four complete oscillations. If a periodic force of 150 cos 50t is applied to the mass in vertical direction, (a) Find the amplitude of the forced vibration (b) What is its amplitude at resonance? (c) Comment on the results obtained in part (a) and (b) (15 markah/marks)
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mi+ci +kx- Asin(ot) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor un-damped natural frequency on a. and the
A second order mechanical system of a...
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.
Can
I get help with this
2. (20 points) The damped single degree-of-freedom mass-spring system shown below has a mass m- 20 kg and a spring stiffness coefficient k 2400 N/m. a) Determine the damping coefficient of the system, if it is given that the mass exhibits a response with an amplitude of 0.02 m when the support is harmonically excited at the natural frequency of the system with an amplitude Yo-0.007 m b) Determine the amplitude of the dynamic...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
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 damped system consists of a mass (m = 30kg) supported on a spring and a damper in parallel. In an experiment, the period of vibration of this system was measured to be 0.5 seconds, and the ratio of maximum displacement between two successive cycles was determined from the experimental data to be 20. Determine: a. The logarithmic decrement. [2] Q4a. Answer: b. The damping ratio, commenting if this is over-damped, critically damped, or under-damped. [4] Q4b. Answer: c. The...
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...
ineers can determine properties of a structure that is modeled as damped spring oscillator-such as a bridge-by applying a driving force to it. A weakly damped spring oscillator of mass 0.242 kg is driven by a sinusoidal force at the oscillator's resonance frequency of 34.0 Hz. Find the value of the spring constant Number N/ m The amplitude of the driving force is 0.471 N and the amplitude of the oscillator's steady-state motion in response to this driving force is...
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