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Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely.and there should not be any damper
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Problem 9: What type of motion is termed a free vibration? natural, undamped (B natural, damped...
Problem 15: What type of valve is used to prevent flow reversal? check valve (O plug...
Problem 15: What type of valve is used to prevent flow reversal? check valve (O plug valve C ball valve B butterfly valve Correct answer is marked, Please give detailed explanation on how to arrive to the answer
Single Degree of Freedom -Free Damped Vibration of Machines and Vibrations problem shows a lever ...
Single Degree of Freedom -Free Damped Vibration of Machines and Vibrations problem shows a lever with spring, mass and damper system. The lever has a moment p9 shows a lever with Agure so kgm2 pivoted at point O with a pulley of mass 4 kg with a radius r-0.5 m Vibration and and load mp4 kg. The load stioping between the puiley and cable supporting the load m. The stiffiess coefficient sippie spring isk=2x105 N/m. Calculate the following when the...
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example of a damped harmonic oscillator in practice. Sketch the os...
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example of a damped harmonic oscillator in practice. Sketch the oscilla- tions it undergoes, and calculate their frequency and damping rate for a natural (undamped) frequency wo 10 Hz and damping coefficient γ-: 2.0 s-1
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example...
Question 4 The equation of motion of a forced vibration problem is given by d-x dx,...
Question 4 The equation of motion of a forced vibration problem is given by d-x dx, m- *+kx = Pcos(wt) dt? dt Given the values, m = 6.45, r = 67.42, k = 398.01, P = 5.6 and W = 6.42. Determine the steady-state solution, xp(15.12) of the differential equation, giving your answer correct to 3 decimal places.
Problem zu a constant-volume process, the temperature of a perfect gas changes from T to 1;....
Problem zu a constant-volume process, the temperature of a perfect gas changes from T to 1;. The change in entropy of the gas is proportional to which of the following expressions? T2-1, (T)( T in TzT, OTT Correct answer is marked, please give detailed explanation on how to arrive to the answer
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0...
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0 2 (a) Determine the natural frequency of the unforced system (b) Find the solution (t) forw1 (c) Plot the solution x(t) versus t for w = 0.7, 0.8, and 0.9. (Feel free to use technology. MatLab, Mathematica, etc.) Describe how the response (t) changes as w varies in this interval. What happens as w takes values closer and closer to 1? Briefly explain why...
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from...
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from the roots of the equation: ET Cantilever beam Wn = (k~L)2 VPALA in which E = 2.0 x 1011 N/m is the elastic modulus, L = 0.45 m is the beam length, 1 = 4.5 x 10-11 m is the moment of inertia, A = 6.0 x 10-5 mº is the cross-sectional area, and p = 6850 kg/m' is the density per unit length....
#40 a-f B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on...
#40 a-f
B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
6. A second order differential equation d?x/dt+ 5 dx/dt+7x = 7y. State the undamped natural frequ...
6. A second order differential equation d?x/dt+ 5 dx/dt+7x = 7y. State the undamped natural frequ damping ratio. 7. State the damped natural frequency, damping coefficient and time constant for question 6. 8. Given that the transfer function G is K/s(s+sT). State the type and order of the system 9. It is given that G(s) = K/s (1+sT). This system is operated in a closed-loop with unity feedback. W order and the type of closed-loop system? 10. Given the transfer...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of a block with mass 2 kg hanging from a spring with stiffness 100 N/m. The block is fully immersed in the liquid and based on the properties of the liquid, you have determined experimentally that the drag force (damping force) on the block has a magnitude of 0.91*] where x is velocity and 0.9 has units (Ns/m). Assume positive displacement of the block is...
Problem 15: What type of valve is used to prevent flow reversal? check valve (O plug valve C ball valve B butterfly valve Correct answer is marked, Please give detailed explanation on how to arrive to the answer
Single Degree of Freedom -Free Damped Vibration of Machines and Vibrations problem shows a lever with spring, mass and damper system. The lever has a moment p9 shows a lever with Agure so kgm2 pivoted at point O with a pulley of mass 4 kg with a radius r-0.5 m Vibration and and load mp4 kg. The load stioping between the puiley and cable supporting the load m. The stiffiess coefficient sippie spring isk=2x105 N/m. Calculate the following when the...
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example of a damped harmonic oscillator in practice. Sketch the oscilla- tions it undergoes, and calculate their frequency and damping rate for a natural (undamped) frequency wo 10 Hz and damping coefficient γ-: 2.0 s-1
7. (a) Explain what is meant by damped harmonic motion, and write down a differential equation describing this phenomenon b) Give an example...
Question 4 The equation of motion of a forced vibration problem is given by d-x dx, m- *+kx = Pcos(wt) dt? dt Given the values, m = 6.45, r = 67.42, k = 398.01, P = 5.6 and W = 6.42. Determine the steady-state solution, xp(15.12) of the differential equation, giving your answer correct to 3 decimal places.
Problem zu a constant-volume process, the temperature of a perfect gas changes from T to 1;. The change in entropy of the gas is proportional to which of the following expressions? T2-1, (T)( T in TzT, OTT Correct answer is marked, please give detailed explanation on how to arrive to the answer
Consider the forced but undamped system described by the initial value problem 3cosuwt, (0) 0, (0 2 (a) Determine the natural frequency of the unforced system (b) Find the solution (t) forw1 (c) Plot the solution x(t) versus t for w = 0.7, 0.8, and 0.9. (Feel free to use technology. MatLab, Mathematica, etc.) Describe how the response (t) changes as w varies in this interval. What happens as w takes values closer and closer to 1? Briefly explain why...
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from the roots of the equation: ET Cantilever beam Wn = (k~L)2 VPALA in which E = 2.0 x 1011 N/m is the elastic modulus, L = 0.45 m is the beam length, 1 = 4.5 x 10-11 m is the moment of inertia, A = 6.0 x 10-5 mº is the cross-sectional area, and p = 6850 kg/m' is the density per unit length....
#40 a-f
B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
6. A second order differential equation d?x/dt+ 5 dx/dt+7x = 7y. State the undamped natural frequ damping ratio. 7. State the damped natural frequency, damping coefficient and time constant for question 6. 8. Given that the transfer function G is K/s(s+sT). State the type and order of the system 9. It is given that G(s) = K/s (1+sT). This system is operated in a closed-loop with unity feedback. W order and the type of closed-loop system? 10. Given the transfer...
Problem 2 (20%) Free Vibration with Velocity Dependent Force. Consider a 1 DOF system consisting of a block with mass 2 kg hanging from a spring with stiffness 100 N/m. The block is fully immersed in the liquid and based on the properties of the liquid, you have determined experimentally that the drag force (damping force) on the block has a magnitude of 0.91*] where x is velocity and 0.9 has units (Ns/m). Assume positive displacement of the block is...
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