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7. 150 points) A one-degree-of-freedom system is shown below. (a) (50 points) Derive the differential equation...
3) For the single degree of freedom system shown below: a) Use the equivalent system method...
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
04: Derive the differential equation governing the motion of the one degree-of-freedom system by using Newton's...
04: Derive the differential equation governing the motion of the one degree-of-freedom system by using Newton's method. Use the generalized coordinates shown in figure (5) (bar moment of inertia, 1-2 ml) Slender bar of mass m Figure (5)
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping...
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
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...
A one-degree-of-freedom system has the following equation of motion 12)L cos where ki, k2 and k3...
A one-degree-of-freedom system has the following equation of motion 12)L cos where ki, k2 and k3 are known spring constants, L is a known length, is the generalized coordinate to describe the dynamical behavior of the system, c is a known damping constant. 1. Linearize equation 1 with respect to 0. 14 Points 2. Using the linearized equation previously obtained, calculate the natural circular frequency wn and the natural cyclical frequency f, [14 Points 3. Using the linearized equation previously...
8. + 0.5/1 points Previous Answers OSUniPhys1 15.5.WA.046. My Note A vertical spring-mass system undergoes damped oscil...
8. + 0.5/1 points Previous Answers OSUniPhys1 15.5.WA.046. My Note A vertical spring-mass system undergoes damped oscillations due to air resistance. The spring constant is 2.50 x 10 N/m and the mass at the end of the spring is 15.0 kg. (a) If the damping coefficient is b = 4.50 N. s/m, what is the frequency of the oscillator? 6.498 ✓ Hz (b) Determine the fractional decrease in the amplitude of the oscillation after 7 cycles. 316 x What is...
Can I get help with this 2. (20 points) The damped single degree-of-freedom mass-spring system shown...
Can
I get help with this
2. (20 points) The damped single degree-of-freedom mass-spring system shown below has a mass m- 20 kg and a spring stiffness coefficient k 2400 N/m. a) Determine the damping coefficient of the system, if it is given that the mass exhibits a response with an amplitude of 0.02 m when the support is harmonically excited at the natural frequency of the system with an amplitude Yo-0.007 m b) Determine the amplitude of the dynamic...
For the system shown below, find a) the modeling equation in x; b) natural frequency; c)...
For the system shown below, find a) the modeling equation in x; b) natural frequency; c) damping ratio; d) frequency ratio; e) Magnification factor and f) Steady-state amplitude. M, sin or m = 10 kg 1 = 0.1 kg-m = 10 cm k = 1.6 x 10 **640 N. M = 2 zie " * = 180 rad
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 =...
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
3) For the single degree of freedom system shown below: a) Use the equivalent system method to derive the differential equation governing the motion of the system, taking χ as the Slender har of mass m generalized coordinate. Rigid 1 link b) If m-6 kg, M = 10 kg, and k=500 N/m, determine the value of c that makes the system critically damped. c) For the values obtained in part (b), determine the response of the system, x(t) if x(0)=...
04: Derive the differential equation governing the motion of the one degree-of-freedom system by using Newton's method. Use the generalized coordinates shown in figure (5) (bar moment of inertia, 1-2 ml) Slender bar of mass m Figure (5)
1.- Starting from the differential equation for a 1-degree of freedom system with mass M, damping c and spring stiffness k: a.- Show that the particular solution for the equation with an applied force fo cos(ot), i.e., Mä+ci+kx=f, cos(or) can be expressed as x )= A cos(ot) + A, sin(or) and find the values of A, and A, that solve the differential equation in terms of M, c, k and fo. 5 points. b. Use the result from part a...
A one-degree-of-freedom system has the following equation of motion 12)L cos where ki, k2 and k3 are known spring constants, L is a known length, is the generalized coordinate to describe the dynamical behavior of the system, c is a known damping constant. 1. Linearize equation 1 with respect to 0. 14 Points 2. Using the linearized equation previously obtained, calculate the natural circular frequency wn and the natural cyclical frequency f, [14 Points 3. Using the linearized equation previously...
8. + 0.5/1 points Previous Answers OSUniPhys1 15.5.WA.046. My Note A vertical spring-mass system undergoes damped oscillations due to air resistance. The spring constant is 2.50 x 10 N/m and the mass at the end of the spring is 15.0 kg. (a) If the damping coefficient is b = 4.50 N. s/m, what is the frequency of the oscillator? 6.498 ✓ Hz (b) Determine the fractional decrease in the amplitude of the oscillation after 7 cycles. 316 x What is...
Can
I get help with this
2. (20 points) The damped single degree-of-freedom mass-spring system shown below has a mass m- 20 kg and a spring stiffness coefficient k 2400 N/m. a) Determine the damping coefficient of the system, if it is given that the mass exhibits a response with an amplitude of 0.02 m when the support is harmonically excited at the natural frequency of the system with an amplitude Yo-0.007 m b) Determine the amplitude of the dynamic...
For the system shown below, find a) the modeling equation in x; b) natural frequency; c) damping ratio; d) frequency ratio; e) Magnification factor and f) Steady-state amplitude. M, sin or m = 10 kg 1 = 0.1 kg-m = 10 cm k = 1.6 x 10 **640 N. M = 2 zie " * = 180 rad
Problem 2 (25 points): Consider an undamped single-degree-of-freedom system with k = 10 N/m, 41 = 10 N 92 = 8N, and m = 10 kg subjected to the harmonic force f(t) = qı sin(vt) + 92 cos(vt), v = 1 rad/ sec. Assume zero initial conditions (0) = 0 and c(0) = 0. Derive and plot the analytical solution of the displacement of the system. mm m = f(t) WWWWWWWW No friction Problem 2 Problem 3 (30 points): Using...
F Fosin t m k 2 Figure Qla: System is subjected to a periodic force excitation (a) Derive the equation of motion of the system (state the concepts you use) (b) Write the characteristic equation of the system [4 marks 12 marks (c) What is the category of differential equations does the characteristic equation [2 marks fall into? (d) Prove that the steady state amplitude of vibration of the system is Xk Fo 25 + 0 marks (e) Prove that...
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