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Figure 1 shows a slender beam pivoted at point O. Its mass moment of inertia, taken...
Example 24 A beam of length L and mass m, is pivoted at one end and...
Example 24 A beam of length L and mass m, is pivoted at one end and suspended from a spring of stiffness k distance L from the pivot. A dashpot is also positioned a distance R from the pivot. Show how the equation of motion below can be derived. de 3cR2 de dt 3kLi 0 = 0 mL2 mL dt where x is the displacement at the free end, and c is the damping coefficient (Ns/m)
Example 24 A beam...
The undamped pendulum pivoted at point O shown in Figure E3.48 has a cylinder of mass...
The undamped pendulum pivoted at point O shown in Figure E3.48
has a cylinder of mass m2 at its top that rotates without slipping
on the interior of a cylinder. At the bottom end of the pendulum, a
mass m1 is attached. The rod connecting the two masses is rigid and
weightless. The system is in equilibrium at theta = 0. Determine an
expression for the
period of oscillation of the system. Assume that m2L2 < m1L1.
(Using Lagrange's method)...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displ...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displacement of the top of the tower b) Determine the damped natural frequency, fa (in Hz) of the tower (10 marks) ) A radar device, which inckdes a large rotaling eccentic mass, has been (30 marks) nstalled at the top of the tower Unfortunately, it has a trequency of rotation...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg is connected with a spring with stiffness k = 2000N/m and a damper with damping ratio š = 0.3. The bar is rotating about a point that is 10cm from the left end. (1) Calculate the total kinetic energy and total potential energy. (2) Derive the equation of motion using energy based approach. (3) Determine the undamped natural frequency and damped natural frequency of...
I want matlab code. 585 i1 FIGURE P22.15 22.15 The motion of a damped spring-mass system (Fig. P22.15) is de...
I want matlab code.
585 i1 FIGURE P22.15 22.15 The motion of a damped spring-mass system (Fig. P22.15) is described by the following ordinary differ- ential equation: dx dx in dt2 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 (underdamped), 40 (critically damped), and 200 (over- damped). The spring constant k-20 N/m. The initial ve- locity is...
1. Consider a beam pivoted at point A with a cantilevered end at B. The weight...
1. Consider a beam pivoted at point A with a cantilevered end at B. The weight of the beam is 30-1b, and one end is supported with a vertical spring (k = 1,800 lb/in) compressed 1 inch, to keep it in a horizontal position. If the beam is released from rest at this position, use the conservation of energy method to determine the angular velocity at the instant it becomes vertical. Assume the beam can be treated as a slender...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two per...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connec...
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connected to the ground by a spring that has a stiffness coefficient k. The slider block is subjected to the force F(t), while the rod is subjected to the moment M. Obtain the differential equations of motion of this two-degree-of-freedom...
PROBLEM 3: (40 points) A rigid massless lever ACB, as shown in Figure 3, is pivoting...
PROBLEM 3: (40 points) A rigid massless lever ACB, as shown in Figure 3, is pivoting about point C. A mass mis attached at point A. Assume frictionless pivot point, frictionless pulley, massless pulley, and small angles. The parameters are Ki-30N/m, m=1 kg, K2-40N/m, C-4.35N-s/m, L=0.4 m, a=0.2 m, and b=0.15 m. (i) Draw the Free Body Diagram (FBD) (5 points). (ii) Use Newton's approach to derive the equations of the motion (10 points). (iii) Use Lagrange's method to derive...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
Example 24 A beam of length L and mass m, is pivoted at one end and suspended from a spring of stiffness k distance L from the pivot. A dashpot is also positioned a distance R from the pivot. Show how the equation of motion below can be derived. de 3cR2 de dt 3kLi 0 = 0 mL2 mL dt where x is the displacement at the free end, and c is the damping coefficient (Ns/m)
Example 24 A beam...
The undamped pendulum pivoted at point O shown in Figure E3.48
has a cylinder of mass m2 at its top that rotates without slipping
on the interior of a cylinder. At the bottom end of the pendulum, a
mass m1 is attached. The rod connecting the two masses is rigid and
weightless. The system is in equilibrium at theta = 0. Determine an
expression for the
period of oscillation of the system. Assume that m2L2 < m1L1.
(Using Lagrange's method)...
Design dala Observalion deck mass m-25,000 k Danong ratio 0.5% Figure 91. Determine the equation of motion ofthe ๒wer teevibraorntheform (15 marks) mitt) + car)+xt)- where xt) is the horizontal displacement of the top of the tower b) Determine the damped natural frequency, fa (in Hz) of the tower (10 marks) ) A radar device, which inckdes a large rotaling eccentic mass, has been (30 marks) nstalled at the top of the tower Unfortunately, it has a trequency of rotation...
Question 3 (24 marks) A uniform bar of length L= 1.1m and mass m = 4.2kg is connected with a spring with stiffness k = 2000N/m and a damper with damping ratio š = 0.3. The bar is rotating about a point that is 10cm from the left end. (1) Calculate the total kinetic energy and total potential energy. (2) Derive the equation of motion using energy based approach. (3) Determine the undamped natural frequency and damped natural frequency of...
I want matlab code.
585 i1 FIGURE P22.15 22.15 The motion of a damped spring-mass system (Fig. P22.15) is described by the following ordinary differ- ential equation: dx dx in dt2 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 (underdamped), 40 (critically damped), and 200 (over- damped). The spring constant k-20 N/m. The initial ve- locity is...
1. Consider a beam pivoted at point A with a cantilevered end at B. The weight of the beam is 30-1b, and one end is supported with a vertical spring (k = 1,800 lb/in) compressed 1 inch, to keep it in a horizontal position. If the beam is released from rest at this position, use the conservation of energy method to determine the angular velocity at the instant it becomes vertical. Assume the beam can be treated as a slender...
Exercises 1. (introduction) Sketch or plot the displacement of the mass in a mass-spring system for at least two periods for the case when Wn-2rad/s, 괴,-1mm, and eto =-v/5mm/s. 2. (introduction) The approximation sin θ ะ θ is reasonable for θ < 10°. If a pendulum of length 0.5m, has an initial position of 0()0, what is the maximum value of the initial angular velocity that can be given to the pendulum without violating this smll angle approximation? 3. (harmonic...
44. The system shown in Fig. P7 consists of a slider block of mass m2 and a uniform slender rod of mass m3, length 13, and mass moment of inertia about its center of mass J The slider block is connected to the ground by a spring that has a stiffness coefficient k. The slider block is subjected to the force F(t), while the rod is subjected to the moment M. Obtain the differential equations of motion of this two-degree-of-freedom...
PROBLEM 3: (40 points) A rigid massless lever ACB, as shown in Figure 3, is pivoting about point C. A mass mis attached at point A. Assume frictionless pivot point, frictionless pulley, massless pulley, and small angles. The parameters are Ki-30N/m, m=1 kg, K2-40N/m, C-4.35N-s/m, L=0.4 m, a=0.2 m, and b=0.15 m. (i) Draw the Free Body Diagram (FBD) (5 points). (ii) Use Newton's approach to derive the equations of the motion (10 points). (iii) Use Lagrange's method to derive...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
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