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A certain physical system is described by the 2nd-order ordinary differential equation +6-0. dt (a) Determine...
Y(s) 4 3. Consider a second order system_ and undamped natural frequency. Is the system underdamped,...
Y(s) 4 3. Consider a second order system_ and undamped natural frequency. Is the system underdamped, overdamped or critically damped? [5pts] What are the damping ratio U(s) s2+3s +4
1) Derive the 2d order differential equation for the circuit and solve the equation for a...
1) Derive the 2d order differential equation for the circuit and solve the equation for a natural response and a forced response using initial conditions. Do not use Laplace Transforms. After finding the differential equation, classify the system as critically damped, overdamped, or underdamped and derive the response equation. 12 V 20㏀ 10 mH
Characteristic equation
The voltage ?1 (?) in a network is defined by the equation ? 2?1 (?) /?? 2 + 4 ??1 (?) /?? + 5?1 (?) = 0 (a) Write down the characteristic equation of the network(b) Determine the network’s natural frequencies s1 and s2.(c) If the network is overdamped, or critically damped state the values of the damping term, , and the undamped natural frequency, ?0 If the network is underdamped, state the values of the damping term, , and the...
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: For the following general form of a second order measurement system (Eq. 1), classify...
Problem 2: For the following general form of a second order measurement system (Eq. 1), classify the system as underdamped, critically damped or over damped for each of the sets of coefficients given in parts (a) - (d). Also determine the natural frequency (n), the damping ratio (0 and if possible, the ringing frequency (od). (b) k 25, c 44, m- 3 (c) k 125, c 235, m 1100 (d) k 18, c 24, m 8
For the following ODEs, find roots λ of their characteristics equation and determine the type of damping
a) For the following ODEs, find roots λ of their characteristics equation and determine the type of damping (overdamped, undamped, underdamped, critically damped). For undamped and underdamped cases, find their angular frequency and period (14 points)i) y''+6 y'+10 y=0ii) 4 y''+8 y'+3 y=0iii) y''+8 y'+16 y=0b) Find the general solution for the following ODE 16 y''+8 y'+y=0(6 points)c) Find the particular solution of b) if y(0)=2 and y'(0)=2.5 .(5 points)
HZ A mass of 0.4 kg is suspended from a spring of stiffness 0.4 N/mm. The...
HZ A mass of 0.4 kg is suspended from a spring of stiffness 0.4 N/mm. The damping is 3.794733192 kg/s What is the undamped natural frequency of the system in Hz? f= Your answer should be accurate to within +/-0.1. What is the value of the critical damping coefficient? Сст в kg/s Your answer should be accurate to within +/-0.1. What is the value of the damping ratio? Your answer should be accurate to within +/-0.01. Is the system: (a)...
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to...
solve for #2
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial conditions. Derive a response equation x(t) for the following four cases. a. 5 pts. 0 (no damping) b. 10 pts. 0<1 (underdamped) c. 5 pts. >1 (overdamped) d. 5 pts. ๕-1 (critically damped) Here the is the damping ratio of the oscillating system. [2] 5 pts. For the same system of underdamped case with initial conditions...
Answer last four questions 1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500...
Answer last four questions
1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500 N/m and damping coefficient of 200 kg/s. i) Calculate the undamped natural frequency ii) Calculate the damping ratio iii) Calculate the damped natural frequency iv) Is the system overdamped, underdamped or critically damped? v) Does the solution oscillate? The system above is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. vi) Calculate the form of the response and...
Solve it with matlab 25.16 The motion of a damped spring-mass system (Fig. P25.16) is described...
Solve it with matlab
25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d’x dx ++ kx = 0 m dr dt where x = displacement from equilibrium position (m), t = time (s), m 20-kg mass, and c = the damping coefficient (N · s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m....
Y(s) 4 3. Consider a second order system_ and undamped natural frequency. Is the system underdamped, overdamped or critically damped? [5pts] What are the damping ratio U(s) s2+3s +4
1) Derive the 2d order differential equation for the circuit and solve the equation for a natural response and a forced response using initial conditions. Do not use Laplace Transforms. After finding the differential equation, classify the system as critically damped, overdamped, or underdamped and derive the response equation. 12 V 20㏀ 10 mH
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: For the following general form of a second order measurement system (Eq. 1), classify the system as underdamped, critically damped or over damped for each of the sets of coefficients given in parts (a) - (d). Also determine the natural frequency (n), the damping ratio (0 and if possible, the ringing frequency (od). (b) k 25, c 44, m- 3 (c) k 125, c 235, m 1100 (d) k 18, c 24, m 8
a) For the following ODEs, find roots λ of their characteristics equation and determine the type of damping (overdamped, undamped, underdamped, critically damped). For undamped and underdamped cases, find their angular frequency and period (14 points)i) y''+6 y'+10 y=0ii) 4 y''+8 y'+3 y=0iii) y''+8 y'+16 y=0b) Find the general solution for the following ODE 16 y''+8 y'+y=0(6 points)c) Find the particular solution of b) if y(0)=2 and y'(0)=2.5 .(5 points)
HZ A mass of 0.4 kg is suspended from a spring of stiffness 0.4 N/mm. The damping is 3.794733192 kg/s What is the undamped natural frequency of the system in Hz? f= Your answer should be accurate to within +/-0.1. What is the value of the critical damping coefficient? Сст в kg/s Your answer should be accurate to within +/-0.1. What is the value of the damping ratio? Your answer should be accurate to within +/-0.01. Is the system: (a)...
solve for #2
[1] 25 pts. A damped single degree of freedom system without applied forces is oscillating due to a certain unknown initial conditions. Derive a response equation x(t) for the following four cases. a. 5 pts. 0 (no damping) b. 10 pts. 0<1 (underdamped) c. 5 pts. >1 (overdamped) d. 5 pts. ๕-1 (critically damped) Here the is the damping ratio of the oscillating system. [2] 5 pts. For the same system of underdamped case with initial conditions...
Answer last four questions
1. A spring-mass-damper system has mass of 150 kg, stiffness of 1500 N/m and damping coefficient of 200 kg/s. i) Calculate the undamped natural frequency ii) Calculate the damping ratio iii) Calculate the damped natural frequency iv) Is the system overdamped, underdamped or critically damped? v) Does the solution oscillate? The system above is given an initial velocity of 10 mm/s and an initial displacement of -5 mm. vi) Calculate the form of the response and...
Solve it with matlab
25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: d’x dx ++ kx = 0 m dr dt where x = displacement from equilibrium position (m), t = time (s), m 20-kg mass, and c = the damping coefficient (N · s/m). The damping coefficient c takes on three values of 5 (under- damped), 40 (critically damped), and 200 (overdamped). The spring constant k = 20 N/m....
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