Homework Answers
Correct option is 'D' 600 Ns/m. Above problem
can be solved by direct relations of critical damoed systems to the
frequency of undamped vibrations. Critical damping is the damping
when system comes to zero amplitude in minimum time.
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In the shown system, the bar AB has a mass of 100 kg, the constant of...
Figure 1 shows a system comprising a bar with mass m=12 kg and the length of...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg....
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg. Its free response amplitude decays such that the amplitude of the 30th cycle is 20% of the amplitude of the 1st cycle. It takes 60 sec to complete 30 cycles. Estimate the damping constant c and the spring constant k.
The figure shows the mass m at the end of a bar of length / is...
The figure shows the mass m at the end of a bar of length / is restrained by a spring and dashpot. The mass is initially at rest and vibrates in the vertical plane under the action of the force F(1). Determine the equation of motion, natural frequency, and damping ratio of the system when m = 45 kg, k = 9700 N/m, c = 950 N.s/m, a - 0.8 m, and I = 2 m. Neglect the mass of...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with dam...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with damping constant gy 2 connected (1) Find the total kinetic energy and total pot of the ystem,e total kinetic edamping constonnected with a spring with system. (2) Derive the equation of motion using e (3) Determine the undamped natural fir 4) Calculate the damping ratio of the sy nergy metho frequency of the system. Gven
L. 2 uestion 3...
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer func...
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer function as: 1/(M*s^2 + B*s + K). With values mass M = 0.67538 kg, friction coefficient B = 1.8951 Ns/M, spring constant K = 322.278 N/M, and Damping coefficient d=2.54821 Ns/m. I know the Open loop system model is: (1/(0.6738s^2 + 1.89515s + 322.278)) = (1.481/(s^2+2.806s+4.772)) Implement a simple controller using only one mass (+spring + damper) so the control is critically damped
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer function...
On a ECP Rectilinear Plant (1 DOF system) mass-spring-damper system, I am given the transfer function as: 1/(M*s^2 + B*s + K). With values mass M = 0.67538 kg, friction coefficient B = 1.8951 Ns/M, spring constant K = 322.278 N/M, and Damping coefficient d=2.54821 Ns/m. I know the Open loop system model is: (1/(0.6738s^2 + 1.89515s + 322.278)) = (1.481/(s^2+2.806s+4.772)) Implement a simple controller using only one mass (+spring + damper) so the control is critically damped
A block weighing 4 kg is supported by a spring with a constant of k =...
A block weighing 4 kg is supported by a spring with a constant
of k = 128 N/m and a dashpot with a coefficient of viscous
damping of c = 0.6 N·s/m. The block is in equilibrium when
it is struck from below by a hammer that imparts to the block an
upward velocity of 0.4 m/s.
Determine the maximum upward displacement of the block from
equilibrium after two cycles.
The maximum upward displacement is _ mm.
Required information NOTE:...
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.
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s...
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed...
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
Figure 1 shows a system comprising a bar with mass m=12 kg and
the length of the bar L=2 m, two springs with stiffness k_t=1000
N-m/rad and k=2000 N/m, one damper with damping coefficient c=50
N-s/m and two additive masses at the end of the bar, where each
mass (M) is equal to 50 kg. The rotation about the hinge A,
measured with respect to the static equilibrium position of the
system is θ(t). The system is excited by force...
Question 6 (Second-order system - log decrement). A mass-spring-damper system has a mass of 100 kg. Its free response amplitude decays such that the amplitude of the 30th cycle is 20% of the amplitude of the 1st cycle. It takes 60 sec to complete 30 cycles. Estimate the damping constant c and the spring constant k.
The figure shows the mass m at the end of a bar of length / is restrained by a spring and dashpot. The mass is initially at rest and vibrates in the vertical plane under the action of the force F(1). Determine the equation of motion, natural frequency, and damping ratio of the system when m = 45 kg, k = 9700 N/m, c = 950 N.s/m, a - 0.8 m, and I = 2 m. Neglect the mass of...
L. 2 uestion 3 (20 marks) A rotating bar of length L and mass m stiffness k and a damper with damping constant gy 2 connected (1) Find the total kinetic energy and total pot of the ystem,e total kinetic edamping constonnected with a spring with system. (2) Derive the equation of motion using e (3) Determine the undamped natural fir 4) Calculate the damping ratio of the sy nergy metho frequency of the system. Gven
L. 2 uestion 3...
A block weighing 4 kg is supported by a spring with a constant
of k = 128 N/m and a dashpot with a coefficient of viscous
damping of c = 0.6 N·s/m. The block is in equilibrium when
it is struck from below by a hammer that imparts to the block an
upward velocity of 0.4 m/s.
Determine the maximum upward displacement of the block from
equilibrium after two cycles.
The maximum upward displacement is _ mm.
Required information NOTE:...
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.
1) A railroad car of mass 2,000 kg traveling at a velocity v = 10 m/s is stopped at the end of the tracks by a spring-damper system, as shown below. If the stiffness of the spring is k= 40 N/mm and the damping constant c 20 N-s/mm, determine (a) the maximum displacement of the car after engaging the springs and damper, (b) the time taken to reach maximum displacement k2 P 0000 k/2
1) A railroad car of mass...
Problem 1 (Harmonic Oscillators) A mass-damper-spring system is a simple harmonic oscillator whose dynamics is governed by the equation of motion where m is the mass, c is the damping coefficient of the damper, k is the stiffness of the spring, F is the net force applied on the mass, and x is the displacement of the mass from its equilibrium point. In this problem, we focus on a mass-damper-spring system with m = 1 kg, c-4 kg/s, k-3 N/m,...
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