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For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - ...
Please show work 3. Given a mass-spring-damper system, the 2kg mass is connected to two linear...
Please show work
3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
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.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a s...
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
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...
(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
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the d...
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and the constants in the applied force? Assume it is an underdamped system.
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and...
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.
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness...
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k....
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Consider the spring-mass-damper system shown. Assume M-1kg. B - 20 N-s/m, K-25 N/m and f(t) =...
Consider the spring-mass-damper system shown. Assume M-1kg. B - 20 N-s/m, K-25 N/m and f(t) = ON (zero-input case). The initial conditions are: x(O) = 1 m, x(0) = 0 m/s Select the correct plot of "x vs. t" for this zero-input case. They M B 0 0 O O o
Please show work
3. Given a mass-spring-damper system, the 2kg mass is connected to two linear springs with stiffness coefficients ki- 100 N/m and ki 150 N/m and a viscous damper with b 50 Ns/m. A constant force of SN is applied as shown. The effect of friction is negligible. ki m b 3.1 [2pts] Determine the equivalent stiffness of the springs. 3.2 [3pts] Draw the free-body diagram of the system. Define the generalized coordinate and label your forces and...
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.
A second order mechanical system of a mass connected to a spring and a damper is subjected to a sinusoidal input force mx+cx + kx = A sin(at) The mass is m-5 kg, the damping constant is c = 1 N-sec/m, the spring stiffness is 2 N/m, and the amplitude of the input force is A- 3 N. For this system give explicit numerical values for the damping factor 5 and the un-damped natural frequency Using the given formulas for...
(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
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and the constants in the applied force? Assume it is an underdamped system.
A s Spring (k)-mass (m)- damper (c) system is subject to two impulses: F-2F and F-F escribe the displacement of the mass as a function of time in terms of m,c, k, o, and...
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.
4. (30%) Consider the following system that consists of a mass m-10kg, coil spring of stiffness k-1000N/m, and damping c-200Ns/m. 1) Suppose that the mass is initially at rest and is given an initial velocity of 3 m/s Find the free vibration response of the mass. 2) Suppose that at a later time, a harmonic force F (t)- sin15t is acted on the mass. Determine the amplitude of the forced vibration response. F, sin
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Consider the spring-mass-damper system shown. Assume M-1kg. B - 20 N-s/m, K-25 N/m and f(t) = ON (zero-input case). The initial conditions are: x(O) = 1 m, x(0) = 0 m/s Select the correct plot of "x vs. t" for this zero-input case. They M B 0 0 O O o
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