1.) a) Calculate the natural frequency from a shaft
system. the system has no mass. the length is 2l, two central mass
is "m" and two springs with stiffness "k"
b) Determine the central location or nodal location of the shaft
for each vibration modus!
Homework Answers
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1.) a) Calculate the natural frequency from a shaft
system. the system has no mass. the...
Q1. For the system shown in Figure 1 where the beam with mass m and length...
Q1. For the system shown in Figure 1 where the beam with mass m and length L is connected to the fixed surfaces through three springs with same stiffness k, (i) Calculate the total kinetic energy and total potential energy of the system; (ii) Derive the equation of motion in terms of rotation angle 0; (iii) Find the natural frequency of the system; (iv) Calculate the natural period if the stiffness k of all springs is doubled; (v) If the...
Vibration Engineering Figure Q5(b) shows a motor having mass of 50 kg is mounted on the...
Vibration Engineering
Figure Q5(b) shows a motor having mass of 50 kg is mounted on the cantilever beam of length l = 0.3 m. The motor is supported by two springs of stiffness k = 2 kN/m each. The cantilever is made of steel (stiffness, k = 3E1 Young's modulus E = 209 MPa, moment of inertia, I = 1.5 x 10 kg.m²). i) Determine total stiffness of the system. 7 marks) ii) Determine the natural frequency of the system....
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...
Question 1 - Fundametals of Engineering (PEL QULLUM Determine the natural frequency of the following system....
Question 1 - Fundametals of Engineering (PEL QULLUM Determine the natural frequency of the following system. Assume K-2 N/m, K 3 N/m K, 4 N/m for the top, middle and bottom springs respectively. Also, m-3 kg. Also write the equation of motion for the equivalent stiffness and 3-kg mass, Estimated time: 10 min. Estimated time taken to solve this problem: 10 min. Show all the steps for solving this problem. Do not skip any step. 24 www freccelle famm www...
2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each...
2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each mass is m-5 kg and the linear elastic spring has a constant k 325 N/m.
2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each mass is m-5 kg and the linear elastic spring has a constant k 325 N/m.
5 mm 10 mm 1000 mm I 90 mm Fig. 1: A hollow shaft with a...
5 mm 10 mm 1000 mm I 90 mm Fig. 1: A hollow shaft with a solid circular disc Question 1 For the system shown in Fig. 1, a vertical hollow steel shaft of diameter (d) = 5mm and length (L) = 100mm is fixed at its upper end and has a solid circular disc having a diameter (D) = 90mm and a mass (m) 12kg fixed rigidly to its lower end as shown. Taking G = 83 GN/m2 for...
2. An undamped mass on a spring has a natural frequency of 10Hz. The system consists...
2. An undamped mass on a spring has a natural frequency of 10Hz. The system consists of four identical springs in parallel, and suffers some damage so that one spring is removed, and at the same time the mass is halved. Find the modified natural frequency (in Hz) of the system after damage. [5]
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.
please solve it as soon as possible and be sure of your answers A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k....
please solve it as soon as possible and be sure of
your answers
A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k. If the translational and angular displacements of the cylinder are x and 8 from its equilibrium position. Determine the following: a- Equation o method b- Find the natural frequency of vibration f motion of the system assuming that the system is...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
Q1. For the system shown in Figure 1 where the beam with mass m and length L is connected to the fixed surfaces through three springs with same stiffness k, (i) Calculate the total kinetic energy and total potential energy of the system; (ii) Derive the equation of motion in terms of rotation angle 0; (iii) Find the natural frequency of the system; (iv) Calculate the natural period if the stiffness k of all springs is doubled; (v) If the...
Vibration Engineering
Figure Q5(b) shows a motor having mass of 50 kg is mounted on the cantilever beam of length l = 0.3 m. The motor is supported by two springs of stiffness k = 2 kN/m each. The cantilever is made of steel (stiffness, k = 3E1 Young's modulus E = 209 MPa, moment of inertia, I = 1.5 x 10 kg.m²). i) Determine total stiffness of the system. 7 marks) ii) Determine the natural frequency of the system....
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...
Question 1 - Fundametals of Engineering (PEL QULLUM Determine the natural frequency of the following system. Assume K-2 N/m, K 3 N/m K, 4 N/m for the top, middle and bottom springs respectively. Also, m-3 kg. Also write the equation of motion for the equivalent stiffness and 3-kg mass, Estimated time: 10 min. Estimated time taken to solve this problem: 10 min. Show all the steps for solving this problem. Do not skip any step. 24 www freccelle famm www...
2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each mass is m-5 kg and the linear elastic spring has a constant k 325 N/m.
2. Calculate the EOM (using Newtons 2nd law) and the natural frequency of the spring-mass system shown below. Each mass is m-5 kg and the linear elastic spring has a constant k 325 N/m.
5 mm 10 mm 1000 mm I 90 mm Fig. 1: A hollow shaft with a solid circular disc Question 1 For the system shown in Fig. 1, a vertical hollow steel shaft of diameter (d) = 5mm and length (L) = 100mm is fixed at its upper end and has a solid circular disc having a diameter (D) = 90mm and a mass (m) 12kg fixed rigidly to its lower end as shown. Taking G = 83 GN/m2 for...
2. An undamped mass on a spring has a natural frequency of 10Hz. The system consists of four identical springs in parallel, and suffers some damage so that one spring is removed, and at the same time the mass is halved. Find the modified natural frequency (in Hz) of the system after damage. [5]
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.
please solve it as soon as possible and be sure of
your answers
A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k. If the translational and angular displacements of the cylinder are x and 8 from its equilibrium position. Determine the following: a- Equation o method b- Find the natural frequency of vibration f motion of the system assuming that the system is...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
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