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A mass-spring-damper system is shown below. If a periodic external forceAssume: r acts on the mass...
1. There is a mass-spring-damper system as shown in Fig. 1 (a) Find the total response(x(t)). In ...
1. There is a mass-spring-damper system as shown in Fig. 1 (a) Find the total response(x(t)). In addition, find the transient response and the steady state response in the total response. Assuming, the initial values are zero. (b) Draw the total response using MATLAB or Excel. 2 Ao Fig. 1
1. There is a mass-spring-damper system as shown in Fig. 1 (a) Find the total response(x(t)). In addition, find the transient response and the steady state response in the total...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass of the handle is negligi- ble (only 1 FBD is necessary). Consider the displacement (t) to be the input to the system and the cart displacement az(t) to be the output. You may assume negligible drag. MwSpring-Damper System M0 Problem 3 Repeat problem 2, but with the following differences: • Assume the mass of the handle m, is not equal to zero. You may...
For the system shown below, a 20Kg mass is sitting on a spring-damper system on a foundation. The system is operating a...
For the system shown below, a 20Kg mass is sitting on a spring-damper system on a foundation. The system is operating at a frequency of 20 rad/s with only one unbalanced mass, m. For the maximum transmissibility at (=0.2, use the chart provided below to determine the suitable values for the spring and the damper constants If a second mass is added to the system (m2=m) at an angle 90 degrees behind the first mass, What is the maximum force...
A force transduce r is a mass-spring-damper system. When an external force is applied to the...
A force transduce r is a mass-spring-damper system. When an external force is applied to the mass, the spring displacement is measured that indirectly represents the level of the force. The system dynamics is 8 7 (a) Convert the system dynamics into the standard form +2wnx Kownf by calculating the values of Ko-, ah in terms of the physical parameters M, B, K. (8%) (b) Calculate the transmissyde)l, force. (Hint: write down the transfer function first.) (7%) missibility Trere o...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
3 dismo plesis The spring mass damper system shown is subjected to a force f(t), which...
3
dismo plesis
The spring mass damper system shown is subjected to a force f(t), which is a step function. b m f(t) At time t=0, with zero initial conditions, the system is subjected to the force. The magnitude of the force is 4 newton, while the spring rate is 8.2 newton/meter, and the damping coefficient is 10 newton-sec/meter. Calculate the energy stored in the spring, in Joules, in steady state.
Consider the mass-spring-damper system shown below left. A spring-based force gage, with spring constant Kgage, is...
Consider the mass-spring-damper system shown below left. A
spring-based force gage, with spring constant Kgage, is to be
inserted between the spring K and mass M (as shown below right) to
measure the force in K in response to the applied position xin.
With ftrue representing the force in K without the gage present,
and fgage representing the force in K with the gage present, the
Laplace transforms of fgage and ftrue satisfy
Problem 2.31: An underdamped mass-spring-dashpot system is subject to a periodic force F(t) of a ...
Problem 2.31: Please complete all of the following
Problem 2.31: An underdamped mass-spring-dashpot system is subject to a periodic force F(t) of a period T and a saw-tooth form, as shown in Fig. P2.31. Assume ζ 0.1. AF(t) T" 2T 3T Figure P2.31 Periodic loading of saw-tooth shape (a) Obtain the Fourier series expansion for the force. (b) Find the Fourier series expansion of the system's steady-state response. (c) For T/T, = 0.5, where T, is the natural period of...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k is subject to a force given by Equation 1 above. Determine the steady state response of the system to the above force. f(t) = 3 1-1 - 7/2 <t<o 1 0<t</2 1
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and it...
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...
1. There is a mass-spring-damper system as shown in Fig. 1 (a) Find the total response(x(t)). In addition, find the transient response and the steady state response in the total response. Assuming, the initial values are zero. (b) Draw the total response using MATLAB or Excel. 2 Ao Fig. 1
1. There is a mass-spring-damper system as shown in Fig. 1 (a) Find the total response(x(t)). In addition, find the transient response and the steady state response in the total...
Problem 2 - A modified mass-spring-damper system: Model the modified mass-spring-damper system shown below. The mass of the handle is negligi- ble (only 1 FBD is necessary). Consider the displacement (t) to be the input to the system and the cart displacement az(t) to be the output. You may assume negligible drag. MwSpring-Damper System M0 Problem 3 Repeat problem 2, but with the following differences: • Assume the mass of the handle m, is not equal to zero. You may...
For the system shown below, a 20Kg mass is sitting on a spring-damper system on a foundation. The system is operating at a frequency of 20 rad/s with only one unbalanced mass, m. For the maximum transmissibility at (=0.2, use the chart provided below to determine the suitable values for the spring and the damper constants If a second mass is added to the system (m2=m) at an angle 90 degrees behind the first mass, What is the maximum force...
A force transduce r is a mass-spring-damper system. When an external force is applied to the mass, the spring displacement is measured that indirectly represents the level of the force. The system dynamics is 8 7 (a) Convert the system dynamics into the standard form +2wnx Kownf by calculating the values of Ko-, ah in terms of the physical parameters M, B, K. (8%) (b) Calculate the transmissyde)l, force. (Hint: write down the transfer function first.) (7%) missibility Trere o...
. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1,...
3
dismo plesis
The spring mass damper system shown is subjected to a force f(t), which is a step function. b m f(t) At time t=0, with zero initial conditions, the system is subjected to the force. The magnitude of the force is 4 newton, while the spring rate is 8.2 newton/meter, and the damping coefficient is 10 newton-sec/meter. Calculate the energy stored in the spring, in Joules, in steady state.
Consider the mass-spring-damper system shown below left. A
spring-based force gage, with spring constant Kgage, is to be
inserted between the spring K and mass M (as shown below right) to
measure the force in K in response to the applied position xin.
With ftrue representing the force in K without the gage present,
and fgage representing the force in K with the gage present, the
Laplace transforms of fgage and ftrue satisfy
Problem 2.31: Please complete all of the following
Problem 2.31: An underdamped mass-spring-dashpot system is subject to a periodic force F(t) of a period T and a saw-tooth form, as shown in Fig. P2.31. Assume ζ 0.1. AF(t) T" 2T 3T Figure P2.31 Periodic loading of saw-tooth shape (a) Obtain the Fourier series expansion for the force. (b) Find the Fourier series expansion of the system's steady-state response. (c) For T/T, = 0.5, where T, is the natural period of...
(By hand) Suppose a spring-mass-damper system with mass m, linear damping coefficient cand spring constant k is subject to a force given by Equation 1 above. Determine the steady state response of the system to the above force. f(t) = 3 1-1 - 7/2 <t<o 1 0<t</2 1
Question8 n the spring-mass-damper system in Figure 8, the force F, is applied to the mass and its displacement is measured via r(t), whilst k and c are the spring and damper constants, respectively x(t) Figure 8: A spring-mass-damper system. a) Obtain the differential equation that relates the input force F, to the measured dis- (6 marks) placement x(t) for the system in Figure 8. b) Draw the block diagram representation of the system in Figure 8. c) Based on...
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