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F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
3.23 The system shown in Figure P3.23 is acted upon by the forcing function shown. The...
3.23 The system shown in Figure P3.23 is acted upon by the forcing function shown. The system parameters are m = 15 kg, k = 75 kN/m,fo = 750 N, and o 15.13 Hz. Tasks: For motion about equilibrium, determine the steady-state amplitude and phase: (a) Free vibration tests result in a log dec, 6, of Im 0.523 (b) c=0. (c) Using the damping from part (a), determine ft)-fo cos ot the range of excitation frequencies such that the amplitude...
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...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A 100 [kg] reciprocating internal combustion engine is fitted to a thin, massless beam using a...
A 100 [kg] reciprocating internal combustion engine is fitted to a thin, massless beam using a vibrations damper. It is known that a machine with a rotating unbalance experiences a frequency squared harmonic excitation. The magnitude of the rotating unbalance is A = m,e = 0.3 [kg. m). 1. Calculate the nondimensional function for the state that has a steady state amplitude of 10 [mm] at a 90 [rad/s] speed. 2- Determine the frequency ratio, natural frequency, and the beams...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displ...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displacement of the top of the tower b) Determine the damped natural frequency, fa (in Hz) of the tower (10 marks) ) A radar device, which inckdes a large rotaling eccentic mass, has been (30 marks) nstalled at the top of the tower Unfortunately, it has a trequency of rotation...
A system is described by the following differential equation: Ï + + 4 x = sin(at)...
A system is described by the following differential equation: Ï + + 4 x = sin(at) The steady-state response can be written: Xss = A sinot + 0) If the phase angle is: JT O = radians 2 What is the excitation frequency, o ? rad 0 = 0 S rad w = 1 S rad 0 = 2 S rad 0 = 4
1 T I т I N F The transfer function of a linear differential equation is...
1 T I т I N F The transfer function of a linear differential equation is defined by the Laplace transform of output (response function) over the Laplace transform of input (driving force) The block diagram of a system is not unique. F In the system with the first order differential equation, the steady-state error due to unite step function is not zero. F In a system with a sinusoidal input, the response at the steady state is sinusoidal at...
5.4 Consider the system with a required steady-state error of 20%, K(s + 2) s(s +3s + 5) and an a...
5.4 Consider the system with a required steady-state error of 20%, K(s + 2) s(s +3s + 5) and an adjustable PI controller zero location. KL(s) Show that the corresponding closed-loop characteristic equation is given by s+ a Next, rewrite the equation as 1 + KG(s0 where K K K.a is constant, and Gf(s) is a function of s, and ex amine the effect of shifting the zero on the closed-loop poles. (a) Design the system for a dominant second-order...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
3.23 The system shown in Figure P3.23 is acted upon by the forcing function shown. The system parameters are m = 15 kg, k = 75 kN/m,fo = 750 N, and o 15.13 Hz. Tasks: For motion about equilibrium, determine the steady-state amplitude and phase: (a) Free vibration tests result in a log dec, 6, of Im 0.523 (b) c=0. (c) Using the damping from part (a), determine ft)-fo cos ot the range of excitation frequencies such that the amplitude...
Question B A machine on a viscoelastic foundation (Figure 31.1), modelled as a spring mass-damper system is acted upon by a force modelled as a harmonic force: F(t) = 0.2 sin(wt) Force is given in N and time in seconds. W Figure 31.1 Nos Given numerical values: m = 10 kg C=5 M k = 1000 = 1) draw the correct Free-Body-Diagram and determine the equation of motion [2 marks) 2) determine the natural frequency and the damping ratio of...
A 100 [kg] reciprocating internal combustion engine is fitted to a thin, massless beam using a vibrations damper. It is known that a machine with a rotating unbalance experiences a frequency squared harmonic excitation. The magnitude of the rotating unbalance is A = m,e = 0.3 [kg. m). 1. Calculate the nondimensional function for the state that has a steady state amplitude of 10 [mm] at a 90 [rad/s] speed. 2- Determine the frequency ratio, natural frequency, and the beams...
Olt) 1422LLA 1. The system at the right is subject to the harmonic + x(t) force f(t) = Fo sin ot as shown, with amplitude 50 N and a forcing frequency due to a motor (not m shown) with speed = 191 rotations per minute (RPM). Mass m can only translate horizontally and the rod is pinned at point O. The parameters are: r = 5 cm, m= 10 kg, Jo = 1 kg m-, kı = 1000 N/m, ka...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displacement of the top of the tower b) Determine the damped natural frequency, fa (in Hz) of the tower (10 marks) ) A radar device, which inckdes a large rotaling eccentic mass, has been (30 marks) nstalled at the top of the tower Unfortunately, it has a trequency of rotation...
A system is described by the following differential equation: Ï + + 4 x = sin(at) The steady-state response can be written: Xss = A sinot + 0) If the phase angle is: JT O = radians 2 What is the excitation frequency, o ? rad 0 = 0 S rad w = 1 S rad 0 = 2 S rad 0 = 4
1 T I т I N F The transfer function of a linear differential equation is defined by the Laplace transform of output (response function) over the Laplace transform of input (driving force) The block diagram of a system is not unique. F In the system with the first order differential equation, the steady-state error due to unite step function is not zero. F In a system with a sinusoidal input, the response at the steady state is sinusoidal at...
5.4 Consider the system with a required steady-state error of 20%, K(s + 2) s(s +3s + 5) and an adjustable PI controller zero location. KL(s) Show that the corresponding closed-loop characteristic equation is given by s+ a Next, rewrite the equation as 1 + KG(s0 where K K K.a is constant, and Gf(s) is a function of s, and ex amine the effect of shifting the zero on the closed-loop poles. (a) Design the system for a dominant second-order...
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
2(35%) Consider the system shown below. (a) Derive the equation of motion of the mass m. (b) Find the steady-state displacement of the mass m. (c) Find the force transmitted to the support at P. y()-Ycos wt C2
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