Homework Answers
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
A 5-kg collar A is at rest on top of, but not attached to, a spring...
A 5-kg collar A is at rest on top of, but not attached to, a spring with stiffness k1 = 400 N/m when a constant 150-N force is applied to the cable. Knowing A has a speed of 1 m/s when the upper spring is compressed 75 mm, determine the spring stiffness k2. Ignore friction and the mass of the pulley
1) A silicon cantilever beam with mass = 4 x 10-10 Kg has a spring constant...
1) A silicon cantilever beam with mass = 4 x 10-10 Kg has a spring constant of 31 N/m. Calculate the natural frequency of the beam in Hz. Assume no damping. 2) An atom in a lattice has a resonance frequency of 9.2 THz. According to quantum mechanics, what is the lowest amount of energy this oscillator can have? Express answer in J.
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...
a 5.0 kg mass has a spring, k = 80 N/m, attached to it and it...
a 5.0 kg mass has a spring, k = 80 N/m, attached to it and it is moving at 6.0 m/s to the right. the end with the spring collides with a 10 kg mass that is stationary. determine the maximum compression of the spring
A uniform beam of mass M-100 kg and length 1 2.00 m is suspended from a...
A uniform beam of mass M-100 kg and length 1 2.00 m is suspended from a ceiling at an angle of 30" below the horizontal. The beam is attached to the ceiling by a hinge at one end and a light support rope attached to the other end. What is the magnitude of the force by the hinge? (Enter your answer in units of N. Only enter the number using 2 significant figures.) 30 L = 2.0 m M=10.0 kg
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0...
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
For a cantilever beam with elastic modulus E loaded by a couple M at the free end, the following ...
For a cantilever beam with elastic modulus E loaded by a couple M at the free end, the following stress field is proposed: σ.-Dy, σ,-σ.-TE,-T.-T, CD is a constant) a. Show that this stress field satisfies the three equations of equilibrium and the six compatibility equations. b. Show that the top, bottom, front, and back surfaces are traction free for this set of stresses. c. Show that the resultant normal and shear force are zero on the free end. d....
Problem 5: A cantilever beam AB of length L supports a uniform load of intensity q...
Problem 5: A cantilever beam AB of length L supports a uniform load of intensity q (see figure) has a fixed support at A and spring support at B with rotational stiffness kR. Rotation at B, OB results in a reaction moment MB*Rx θ8. Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), find rotation GB and di the end B. (Hint- You will need third boundary condition so read the problem statement carefully) (20 points)...
3.15 The mechanical system of Figure 3,56 is formed of a point mass m-Oll and two springs of stiffnesses ki - 100 N/m and k2 120 N/m. Its natra frequency is evaluated by means of a cantilever sensor, which is attached to the point mass. Knowing the cantilever has a constant circular cross section, a length 1 0.08 m, the cantilever's Young's modulus is E -200 GPa, and mass density is p 7600 kg/m3, determine its diameter d, such that...
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...
A uniform beam of mass M-100 kg and length 1 2.00 m is suspended from a ceiling at an angle of 30" below the horizontal. The beam is attached to the ceiling by a hinge at one end and a light support rope attached to the other end. What is the magnitude of the force by the hinge? (Enter your answer in units of N. Only enter the number using 2 significant figures.) 30 L = 2.0 m M=10.0 kg
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
Problem: Find the natural frequencies of the system shown in Figure. Take m 2 kg ma 2.5 kg ms 3.0 kg me = 1.5 kg 914 Given: Four degree of freedom spring-mass system with given masses an stiffnesses. Find: Natural frequencies and mode shapes. Approach: Find the eigenvalues and eigenvectors of the dynamical matrix. 1. Determine [m] and [k] matrices of the vibrating system with all details 2. Determine [DI matrix. 3. Determine Natural frequencies and mode shapes analytically 3....
For a cantilever beam with elastic modulus E loaded by a couple M at the free end, the following stress field is proposed: σ.-Dy, σ,-σ.-TE,-T.-T, CD is a constant) a. Show that this stress field satisfies the three equations of equilibrium and the six compatibility equations. b. Show that the top, bottom, front, and back surfaces are traction free for this set of stresses. c. Show that the resultant normal and shear force are zero on the free end. d....
Problem 5: A cantilever beam AB of length L supports a uniform load of intensity q (see figure) has a fixed support at A and spring support at B with rotational stiffness kR. Rotation at B, OB results in a reaction moment MB*Rx θ8. Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), find rotation GB and di the end B. (Hint- You will need third boundary condition so read the problem statement carefully) (20 points)...
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