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Find design parameters of this 4. An optical measurement table is modeled by two springs, K/2...
A team of researchers are working to find a solution to the anticipated global lack of...
A team of researchers are working to find a solution to the anticipated global lack of ventilators. You are asked to solve a vibration problem with the prototype. The system has a mass m = 5 kg, and the moving parts induce a harmonic force F(t) = 57 cos (66 t) N. The damping is negligible, and the system is assumed to start from rest with no velocity. 1. Write the total response of the system x(t) as a function...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
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
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...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0)...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0) m,ž, +b,X, +k, (x2 – x)+k,x, = 0 The displacements Xi and X2 are measured from their respective equilibrium positions. An external force falt) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacement in your sketch. (Hint verify the system model by applying Newton's laws.)
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
Vibrational Motion Introduction If an object is following Hooke’s Law, then Fnet = -kx = ma...
Vibrational Motion Introduction If an object is following Hooke’s Law, then Fnet = -kx = ma Since acceleration is the second derivative of position with respect to time, the relationship can be written as the differential equation: kx = m δ2xδt2/{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mi>m</mi><mo> </mo><mfrac bevelled="true"><mrow><msup><mi>δ</mi><mn>2</mn></msup><mi>x</mi></mrow><mrow><mi>δ</mi><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac></math>"} Methods for solving differential equations are beyond the scope of this course; in fact, a class in differential equations is usually a requirement for a degree in engineering or physics. However, the solution to this particular differential...
Procedure: Materials: 1. apparatus 2. 2 pieces of metal track 3. plastic or metal ball 4....
Procedure: Materials: 1. apparatus 2. 2 pieces of metal track 3. plastic or metal ball 4. timer 5. meter stick 6. micrometer 7. 2 photogates Assemble your ramp as shown in Figure (1) in the next page. Then set up photogates in location 2 and 3. Measure the diameter (in m) of the metal balls (you will need it for speed calculations). Then, measure the weight (mass) of the ball (in kg). To have a better measurement of the time,...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
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
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...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0) m,ž, +b,X, +k, (x2 – x)+k,x, = 0 The displacements Xi and X2 are measured from their respective equilibrium positions. An external force falt) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacement in your sketch. (Hint verify the system model by applying Newton's laws.)
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
Procedure: Materials: 1. apparatus 2. 2 pieces of metal track 3. plastic or metal ball 4. timer 5. meter stick 6. micrometer 7. 2 photogates Assemble your ramp as shown in Figure (1) in the next page. Then set up photogates in location 2 and 3. Measure the diameter (in m) of the metal balls (you will need it for speed calculations). Then, measure the weight (mass) of the ball (in kg). To have a better measurement of the time,...
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