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A guy of mass m is wakeboarding behind a boat with mass mp. The cord that is being used to tow hi...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - ...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
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...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spr...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Problem 4 Problem 3 (35): The particle with mass m is initially at equilibrium. The cord is assum...
Problem 4 Problem 3 (35): The particle with mass m is initially at equilibrium. The cord is assumed to be taut throughout the motion. The system is critically damped with parameters are m = 4 kg and k = 200 N/m. 7n a) (15) Determine the value of the viscous damping coefficient c. b) (10) If at t -0 the mass m is displaced down the incline by a distance xo -0.2 m from the equilibrium position and released with...
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.
The circular disk of 200-mm radis has a mass of 25 kg with centroidal radius of gration k = 175 m...
The circular disk of 200-mm radis has a mass of 25 kg with centroidal radius of gration k = 175 mm and has a cocentric circular groove of 75-mm radius cut into it. A steady free Tis applied at an angle θ 3rto a cord wrapped around the groove as shown. If T 50 N, H,-0.1, and Aa.-008. m 25 kg 175 mm 200 mm 0.10 A -0.08 1. Draw the FBD and the kinetic diagram showing all forces acting...
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...
Please write legibly Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stif...
Please write legibly
Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stiffness k = 17 N/m and a period of 0.945 s. If the system is released from rest 5 cm from it's equilibrium point at to = 0 s, find the trajectory of the position of the mass-spring-damper from it's release until t 3s Figure 3.2: Mass-spring-damper...
The following system is composed by two masses The first mass m, = 21 kg, moving...
The following system is composed by two masses The first mass m, = 21 kg, moving horizontally (x1, positive rightwards) • The second mass m2 = 2.4 kg, moving horizontally (X2. positive rightwards) The first mass is connected to the ground (on the left) by two springs, each with stiffness k = 201 N/m. The second mass is connected to the first mass by another spring, also with stiffness k = 201 N/m. A harmonic force is applied to the...
QUESTION 2 |15 MARKSI (a) Figure 2 shows a collar with a mass, m of 25...
QUESTION 2 |15 MARKSI (a) Figure 2 shows a collar with a mass, m of 25 kg and coefficient of kinetic friction, pk of 0.3. The attached spring has an unstretched length 7=0.15 m and a stiffness k = 55 Nm. (i) Draw the free-body diagram (FBD) of the system when the collar is at point A with applied force, F = 250 N acting at angle 6 = 30° as shown in Figure 2. [4 Marks] (ii) Find the...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
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...
PROBLEM 1 (35 %) The mechanical system in the figure below consists of a disk of radius r, a block of mass m, a spring of stiffness (spring constant) k, and a damper with damping ratio b. The disk has moment of inertia Jabout its center of mass (pivot point O), and the block is subjected to an external force t) as shown in the figure. The spring is unstressed when x 0= 0. Assume small 0. (a) (10 points)...
Problem 4 Problem 3 (35): The particle with mass m is initially at equilibrium. The cord is assumed to be taut throughout the motion. The system is critically damped with parameters are m = 4 kg and k = 200 N/m. 7n a) (15) Determine the value of the viscous damping coefficient c. b) (10) If at t -0 the mass m is displaced down the incline by a distance xo -0.2 m from the equilibrium position and released with...
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.
The circular disk of 200-mm radis has a mass of 25 kg with centroidal radius of gration k = 175 mm and has a cocentric circular groove of 75-mm radius cut into it. A steady free Tis applied at an angle θ 3rto a cord wrapped around the groove as shown. If T 50 N, H,-0.1, and Aa.-008. m 25 kg 175 mm 200 mm 0.10 A -0.08 1. Draw the FBD and the kinetic diagram showing all forces acting...
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...
Please write legibly
Consider an ideal mass-spring-damper system similar to Figure 3.2. Find the damping coefficient of the system if a mass of 380 g is used in combination with a spring with stiffness k = 17 N/m and a period of 0.945 s. If the system is released from rest 5 cm from it's equilibrium point at to = 0 s, find the trajectory of the position of the mass-spring-damper from it's release until t 3s Figure 3.2: Mass-spring-damper...
The following system is composed by two masses The first mass m, = 21 kg, moving horizontally (x1, positive rightwards) • The second mass m2 = 2.4 kg, moving horizontally (X2. positive rightwards) The first mass is connected to the ground (on the left) by two springs, each with stiffness k = 201 N/m. The second mass is connected to the first mass by another spring, also with stiffness k = 201 N/m. A harmonic force is applied to the...
QUESTION 2 |15 MARKSI (a) Figure 2 shows a collar with a mass, m of 25 kg and coefficient of kinetic friction, pk of 0.3. The attached spring has an unstretched length 7=0.15 m and a stiffness k = 55 Nm. (i) Draw the free-body diagram (FBD) of the system when the collar is at point A with applied force, F = 250 N acting at angle 6 = 30° as shown in Figure 2. [4 Marks] (ii) Find the...
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