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3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force F(t) = Fo cosot. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of m.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force...
I. 20% Consider the undamped vibration absorber discussed in class. The excitation frequency is w. Re-derive...
I. 20% Consider the undamped vibration absorber discussed in class. The excitation frequency is w. Re-derive the forced response magnitudes of the main mass and the absorber mass Xa(t) FO)-Fo sin o f tx( as well as the vibration absorber design criterion ma Discuss the effect of absorber mass selection. What if the excitation frequency is equal to the original resonance frequency »,m
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k...
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k and mi-m2-m3-m, determine the natural frequencies and mode shapes. rt
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended ...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
Homework problem! Need help fast Example 2: Figure below shows the principle of a vibration damper....
Homework problem! Need help fast
Example 2: Figure below shows the principle of a vibration damper. The main platform (mass mi) is suspended on a spring/damper system. The suspension has the spring conn Di and the friction coefficient RF. On the platform is a device that produces oscillatioss such as a vibrating sieve (indicated by the dashed box in Figure). The oscillabory force im- posed on the platform by the device can be described as Fit)-Fn(t) D. m. D2 The...
3. Consider a system consisting of a Ikg mass connected to a spring with spring co...
3. Consider a system consisting of a Ikg mass connected to a spring with spring co -ION/. and a friction coefficient of 6N/m, subject to an external force of 15 cos 22 newtons). (a) (5 points) Write down the general solution to this system. myll thy't ny=0 "y"+by't loy=0 F(+)= Iscoszt m 2 tlom +10 - (0) (3 points) Label the steady state response and the transient part of the son above (0) (3 points) is the 3 points) Is...
A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
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...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force F(t) = Fo cosot. (a) Derive the amplitudes of steady-state response for mi and m2. (b) Find the relation between k2 and m2 that leads to no steady state vibration of m.
3. (20%) A vibration absorber, which is a spring-mass system (k2, m2), is added to a system (ki, mi) subject to a harmonic force...
I. 20% Consider the undamped vibration absorber discussed in class. The excitation frequency is w. Re-derive the forced response magnitudes of the main mass and the absorber mass Xa(t) FO)-Fo sin o f tx( as well as the vibration absorber design criterion ma Discuss the effect of absorber mass selection. What if the excitation frequency is equal to the original resonance frequency »,m
2. For the following 3-DOF spring-mass system: (a) Derive the equations of motion. (b) Assuming ki-k2-k3-k and mi-m2-m3-m, determine the natural frequencies and mode shapes. rt
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
3. Consider the spring - mass system shown below, consisting of two masses mi and m2 sus- pended from springs with spring constants ki and k2, respectively. Assume that there is no damping in the system. a) Show that the displacements ai and r2 of the masses from their respective equilibrium positions satisfy the differential equations b) Use the above result to show that the spring-mass system satisfies the following fourth order differential equation and c) Find the general solution...
Homework problem! Need help fast
Example 2: Figure below shows the principle of a vibration damper. The main platform (mass mi) is suspended on a spring/damper system. The suspension has the spring conn Di and the friction coefficient RF. On the platform is a device that produces oscillatioss such as a vibrating sieve (indicated by the dashed box in Figure). The oscillabory force im- posed on the platform by the device can be described as Fit)-Fn(t) D. m. D2 The...
3. Consider a system consisting of a Ikg mass connected to a spring with spring co -ION/. and a friction coefficient of 6N/m, subject to an external force of 15 cos 22 newtons). (a) (5 points) Write down the general solution to this system. myll thy't ny=0 "y"+by't loy=0 F(+)= Iscoszt m 2 tlom +10 - (0) (3 points) Label the steady state response and the transient part of the son above (0) (3 points) is the 3 points) Is...
A spring-mass system has a
spring constant of 3 N/m. A mass of 2 kg is attached to the spring,
and the motion takes place in a viscous fluid that offers a
resistance numerically equal to the magnitude of the instantaneous
velocity. If the system is driven by an external force of (27 cos
3t − 18 sin 3t) N, determine the steady state response. Express
your answer in the form R cos(ωt − δ). (Let u(t) be the
displacement...
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...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
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