0.36 If the mass and the stiffness matrix of the obtained equation is given by M 0.36 50.884 K = -45 -45 50.884
Q: Determine the equivalent spring stiffness constant of the following spring in series and parallel.
A: Given: The stiffness of springs is 250 N/m, 175 N/m and 80 N/m.
Q: Determine the ratio of the shear modulus to the modulus of elasticity of material if the Poisson's…
A: G/E = 0.4
Q: diameter decreases by 0.018 mm during the loading. a) Determine the Poisson's ratio of the material.…
A:
Q: The mass of the block is mc=41 kg and the angle a=33deg. D. mc What is the tension in the cable D,…
A:
Q: Q. for case 3 the end of the fin is insulated so that dT/dx=0 at x=L. and then e-mx emx 1+e-2mL…
A:
Q: A steel bar 300 mm long, 50 mm wide and 40 mm thick is subjected to a pull of 300 kN in the…
A:
Q: Figure 1: y P = 400 kN 30° 1000 mm A Area 30 mm 20 mm In Figure 1, the equilibrium shear force…
A: Given data :- force = 400KN find the shear force at point A.
Q: 7. The stress-strain diagram for polyester resin is shown in the figure. Both strut AB and column…
A:
Q: The weight of the crate is 50 kg and the spring constant is 200 N/m in DB. Use g= 9.81 m/s2.
A:
Q: For many materials, the stress-strain curve can be written by the Ramberg-Osgood equation presented…
A: Given; The strain at 140 MPa, ε140 = 0.04 The strain at 280 MPa, ε280 = 0.1 The strain at 420 MPa,…
Q: Determine the nodal displacement of the bar shown in Figure 1 using two element of equal length. The…
A:
Q: The The composite shaft, consisting of aluminum, copper, and steel sections, is subjected to the…
A:
Q: -lble L ABC kirişinin enine kesiti
A:
Q: 8. The knotted cords in the figure is in equilibrium. Find the tension in each cord that supports a…
A: Given Data Fw=800 N
Q: the stress-strain curve can be written by the Ramberg-Osgood equation presented below, where the…
A:
Q: A loading condition of a beam with parabolic shape is shown below. Using Castigliano's theorem…
A: Consider the diagram shown below with the given variables and reactions as shown below, Here, the…
Q: em as shown below. Assume that all free nodes undergo translation in x (1 DOF at each node) and…
A:
Q: P1. A uniformly tapering circular rod is subjected to load as shown in the figure . Determine the…
A: When an axial load is applied to a bar it tends to get deformed. This elongation depends upon the…
Q: The force P is applied to the bar, which is made from an elastic perfectly plastic material.…
A: Given, Section 1 = AB Length of AB (L1) = 6 in Cross section Area of AB (A1) = 1 in2 Load in AB = P1…
Q: The polyvinyl chloride bar is subjected to an axial force of 900 lb. If it has the original…
A:
Q: The rod is subjected to the linearly varying axial distributed load as shown. What is the correct…
A:
Q: 30, 20 as shear stresses respectively. find the new state of stre and invariant when this element…
A:
Q: Please show complete solutions. Need asap. The series of bars shown have their diameters from left…
A:
Q: Use the stiffness method to calculate the member forces in the structure shown in Figure P1.9. E = 2…
A: Solution solved using is a stiffness method
Q: A loading condition is shown below. Determine the torque (T) required to prevent rotation at the…
A: Since there are two ropes of equal dimensions, the value of tension in both the ropes is the same.…
Q: Determine the equivalent spring stiffness constant of the following spring in series and parallel.…
A:
Q: 2. Auniform bar 3.00 m long is held by ropes at the ends making angle 60.0° and 30.0°, respectively,…
A:
Q: 8) A spring hangs at rest from a support. If you suspend a 0.46 kg mass from the spring it elongates…
A:
Q: The beam is supported by a fixed support at point A. There are 2 distributed loads applied to the…
A:
Q: A simply-supported beam, 9 m in length, is subjected to a uniform load of 20 kN/m applied at the…
A:
Q: . The rigid bar AB is supported by two rods made of the same material. If the bar is horizontal…
A: Given:La=2 ftAa=0.4 in2Lb=3 ftAb=0.2 in2
Q: Use the graphical method to construct the shear-force diagram and identify the magnitude of the…
A: Given- L1 = 14.75ft L2 = 7.75ft Reaction force on point C = 91.50kips Moment on point C =…
Q: 9. The rigid bar AB is supported by two rods made of the same material. The bar is initially…
A:
Q: Determine the equivalent spring stiffness constant of the following spring in series and parallel.…
A:
Q: k2 M2 ki M1 k3 M3 k12 k23 X1 X2 X3 f1 f2 f3
A: Given data To determine the stiffness and elasticity matrices of the system?
Q: The stepped rod is made up of two different materials A and B of lengths 80 cm and 1.2 m…
A:
Q: The steel strip has a unifom thickness of 50 mm. Compute the elongation of the strip caused by the…
A: GIVEN DATA- a=120mm b=50mm t=50mm P=500KN L=1000mm E=200GPa WE HAVE TO FIND TOTAL ELONGATION
Q: Calculate the reaction force on the B support according to the loading shown in the figure. 4 kN/m 2…
A:
Q: The steel block shown in is subjected to a compressive force on all directions. Determine the change…
A: Given data as per question Poisson ratio =0.28 E of steel =210 ×103Nmm2 Δy=-1.3 mm…
Q: Physics for Engineering A uniform bar 3.00 m long is held by ropes at the ends making angle 60.0…
A: Given, W1 = 200 N
Q: 2.0 The rigid beam supports the load of 60 kN. Determine the displacement at 8. Take E = 60 GPa, and…
A: Given data as per question The load applied =60 KN Length of AD =2 m Length of BC =3 m E =60Gpa…
Q: The rod is subjected to an external axial force of 800 N and a uniform distributed load of 100…
A: givenexternal axial force Fa=800Nuniform distributed load w= 100 N/mlength of cantilever beam L=2m
Q: ii, If the length of each element is 5m and the k-EA/Lis given as shown, analyze the following…
A:
Q: What would be the maximum weight W of the block, shown in the following figure, so that the tension…
A:
Q: The rod has a circular cross section. If it is made of an elastic perfectly plastic material,…
A: The shape factor of the round bar is independent of the radius of the cross-section.
Q: For the given figure below, the beam is 57.4 m long. It has a rectangular cross-section area with…
A: Consider the diagram as shown below for the given beam. Here Fs is the spring force.
Q: Q2/ Use the unit load method to find the slope and the horizontal displacement of point C on the…
A:
Q: (2) The strength condition of composition of bending and torsion is _M₂_ √ M² + (aT)² ≤ [0_16] J.= W…
A:
Step by step
Solved in 2 steps with 3 images
- An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = + kx The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) = Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave unknown constants in your equation. x(t) =Consider the mass matrix, 4.00 0.00 0.00 M= 0.00 2.00 0.00 0.00 0.00 1.00 Matrix M is None 2.00 0.00 0.00 M12= 0.00 1.41 0.00 0.00 0.00 1.00 0.30 0.00 0.00 M-1/2=0.00 0.42 0.00 0.00 0.00 0.60) 1.56 0.00 0.00 M-1/2= 0.00 1.10 0.00 0.00 0.00 0.78 0.50 0.00 0.00 M12-0.00 0.71 0.00 0.00 0.00 1.00A square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. 1.0 4. 1.0 3. X- 1.0 1.0 2. 2.
- Equation of motion of a suspension system is given as: Mä(t) + Cx(t) + ax² (t) + bx(t) = F(t), where the spring force is given with a non-linear function as K(x) = ax²(t) + bx(t). %3D a. Find the linearized equation of motion of the system for the motion that it makes around steady state equilibrium point x, under the effect of constant F, force. b. Find the natural frequency and damping ratio of the linearized system. - c. Find the step response of the system ( Numerical values: a=2, b=5, M=1kg, C=3Ns/m, Fo=1N, xo=0.05m1) Consider the baseband pulse x(1) = n(2) = 11 a) Derive the complex ambiguity function for x(t) and compare your result with the one obtained in class. b) Use MATLAB to compute the complex ambiguity function and compare it to part (a). c) Now, consider the pulse x(t) = sinc(Bt) i) Derive the complex ambiguity function for x(t) and compare to the ambiguity function of the rect pulse. Make your observations. ii) Plot the ambiguity function using the mesh function and using the contour function. iii) Use MATLAB to compute the complex ambiguity function and compare it to part (ii).Harmonic oscillators. One of the simplest yet most important second-order, linear, constant- coefficient differential equations is the equation for a harmonic oscilator. This equation models the motion of a mass attached to a spring. The spring is attached to a vertical wall and the mass is allowed to slide along a horizontal track. We let z denote the displacement of the mass from its natural resting place (with x > 0 if the spring is stretched and x 0 is the damping constant, and k> 0 is the spring constant. Newton's law states that the force acting on the oscillator is equal to mass times acceleration. Therefore the differential equation for the damped harmonic oscillator is mx" + bx' + kr = 0. (1) k Lui Assume the mass m = 1. (a) Transform Equation (1) into a system of first-order equations. (b) For which values of k, b does this system have complex eigenvalues? Repeated eigenvalues? Real and distinct eigenvalues? (c) Find the general solution of this system in each case. (d)…
- A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?nk int m The spring-mass-system shown in the figure has the following parameters: spring constant k = 4 N/m; mass m 6 %3D kg and the constant n = 1.6. M is the corresponding mass-matrix of the system. V1 and V2 are the eigenvectors associated with the smallest and largest natural frequencies of the system, respectively. If V,TV, = 1 and V2 V2 = 1, then what is value of V,™MV2 (in kg)? Answer:
- 1. Suppose you are riding your bicycle on a bumpy road having a surface profile that varies harmonically with +/- 6 cm undulations. The distance between consecutive peaks of these undulations is 2 m. When you sit on the seat of your bike for your casual ride, the springs deflect 5 cm. When you are seated, the damper under the seat provides an equivalent linear viscous damping of 10% of the critical damping. A simple representation of your ride on the "never-ending" rough road is shown below. (a) If you are riding your bicycle at a horizontal speed of 2.5 m/sec, how much bumping up and down will you experience? (b) Next day, you are carrying a backpack which increases your on-seat weight by 20%. Assuming that you are still able to ride with same speed, will this "loaded" ride be more or less comfortable than your previous, "no backpack" ride? M k/23 k/2 6 cm 2 m6. The electro-mechanical system shown below consists of an electric motor with input voltage V which drives inertia I in the mechanical system (see torque T). Find the governing differential equations of motion for this electro-mechanical system in terms of the input voltage to the motor and output displacement y. Electrical System puthiy C V V₁ R bac (0) T bac T Motor - Motor Input Voltage - Motor Back EMF = Kbac ( - Motor Angular Velocity - Motor Output Torque = K₂ i Kbacs K₁ - Motor Constants Mechanical System M T Frictionless Support:) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2k