Compute the motion of the block in terms of time, if the block is initially released from position x=2 with zero speed. The parameters are assumed: m=2, b=4, and k=5 x Viscous friction Stiffness k coefficient b Mass m XXXXXX x
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- When a force F acts on a linear spring, the elongation x of the spring is give by F=kx, where k is called the stiffness of the spring. Determine the dimention of k in terms of the base dimention of an absolute (MLT) system of unitswhere k is a positive constant characterizing the stiffness of the spring. Compute the work required to expand the spring from its equilibrium position to length l.Consider the following system: mä (t) + kæ (t) = Fo exp (-at) Assume zero initial conditions. The units are in Newtons. If m = 1 kg. k = 100 N/m, Fo = 40N and a = 5, determine the response of the system at t = 0.1 s. Note: formula for integration Sie-ar sin (b (t – T)) dr = (a sin (bt) – b cos (bt) + bexp (-at)) 0.16 0.25 0.43 0.59 0.35 O0000
- As one stretches a metal wire, which condition is reached first? O the elastic limit the proportional limit O the breaking pointCheck Your Understanding Suppose the mass in Equation 8.6 is doubled while keeping the all other conditions the same. Would the maximum expansion of the spring increase, decrease, or remain the same? Would the speed at point B be larger, smaller, or the same compared to the original mass?A crate of mass m1�1 slides down a well-lubricated hill of height hℎ, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass. a) Write an equation that expresses the speed v of the crate when it arrives at the bottom of the hill in terms of the height of the hill and other known quantities. b) When the two crates collide, they stick together, due to Velcro pads pasted on their mating surfaces. Write an equation that expresses the speed v2 of the two crates after the collision, in terms of the speed v of crate m1 just before the collision. c)As the coupled crates continue to move to the right, they compress the spring by a distance d, at which point they momentarily stop. Assuming that the coefficient of kinetic friction between the…
- A block of mass 5 pounds is placed at the end of a spring, of elastic constant 900 N/m, compressed 1 foot. When the spring is released, the block moves along a horizontal plane and after traveling a distance of 40 inches, it rises along a plane inclined at 30º with the horizontal. There is only friction in the 40-inch section traveled horizontally, the coefficient of friction is 0.1. a. Calculate the distance traveled by the block on the inclined plane if the coefficient of friction between the body and the horizontal plane is 0.1 (there is no friction on the inclined section, nor in the 20 cm). b. State when the kinetic energy will be maximum. end fin start inicio V = 0 μ = 0,1 www 30° V = 03.6 Consider a three-span continuous beam. All supports are pinned supports. Each span has a length of L. The beam has a modulus of elasticity E and a moment of inertia I. All spans are subjected to a uniformly distributed load w. The maximum deflection of the beam occurs in the outer spans and is equal to 0.0069 EI Your job is to evaluate the probability that the deflection will exceed the code-specified limit of L/360 given the following information: L = 5 m (deterministic). w is lognormal with a mean value of 10 kN/m and a coefficient of variation of 0.4. E is lognormal with a mean value of 2 × 107 kN/m² and a coefficient of variation of 0.25. Iis lognormal with a mean value of 8 × 10-4 m² and a standard deviation of 1.5 x 10-4 m*. Calculate the probability of failing the deflection criterion.Isolated system is always at the equilibrium state. True False
- The spring has a stiffness k= 50 lb/ft and an unstretched length of 2 ft. As shown, it is confined by the plate and wall using cables so that its length is 1.5 ft. A 4-lb block is given a speed VA incline having a coefficient of kinetic friction u, = 0.2. If it strikes the plate and pushes it forward 0.25 ft before stopping, determine its speed at A. Neglect the mass of the plate and spring. when it is at A, and it slides down theManually train a linear function he (x) = based on the following training instances using stochastic gradient descent algorithm. The initial values of parameters are 80 = 0.1,0₁ = 0.1, 0₂ = 0.1. The learning rate a is 0.1. Please update each parameter at least five times. X1 0 0 1 1 x₂ 0 1 0 1 y 2 3 3 4A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are u. The block is displaced a distance xo to the right of the unstretched position for the spring and released from rest. If the value for xo is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration a = μg - k/m x, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 10 kg, k = 210 N/m, u = 0.34, and xo = 370 mm and determine the final spring stretch (or compression) xf when the block comes to a complete stop. The distance xf will be positive if to the right (spring stretched) and negative if to the left (spring compressed). Unstretched spring position x xo m