Using superposition Compute the force in the spring as a function of 1, El, w and...
(1 point) Finding the work done in stretching or compressing a spring. Hooke's Law for Springs. According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x) = kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive. Part 1. Suppose that it takes...
1. According to Hooke's law, the force exerted by a spring is proportional to the amount of stretch (or change in length Ax) and is given by F = -KAX, where the minus sign indicates it is a restoring force. If a force of 120 N acts on a mass 250 g attached to a spring of constant K = 54.55 x 103 N/m. Calculate the following: The change in length Ax The angular frequency (w) The frequency (f) The...
1. According to Hooke's law, the force exerted by a spring is proportional to the amount of stretch (or change in length Ax) and is given by F = -KAx, where the minus sign indicates it is a restoring force. If a force of 120 N acts on a mass 250 g attached to a spring of constant K = 54.55 x 10 N/m. Calculate the following: The change in length Ax The angular frequency (w) The frequency (f) The...
For the cantilever beam with a constant El and loading shown, using the superposition method to determine 1) the deflection at B; 2) the slope at B. MWL Mo= 6
find the general solution (y) using laplace transform (1 point) Consider a spring attached to a 1 kg mass, damping constant 8 = 5, and spring constant k = 6 The initial position of the spring is 4 metres beyond its resting length, and the initial velocity is -9 m/s. After 1 second, a constant force of 12 Newtons is applied to the system for exactly 2 seconds Set up a differential equation for the position of the spring y...
PROBLEM 1: Given the overhang beam shown below and subjected to a downward force equal to 20 kN at B. The stiffiess of the beam is El 10 kN-m2 and that of the spring is k (note: F-kA). Determine the value of k such that the deflection at point D due to the 20 kN load is zero. 20 kN 4 m 4 m PROBLEM 1: Given the overhang beam shown below and subjected to a downward force equal to...
1. Determine the reactions at the supports A and B using Force Method. El is constant. w B А L 2 L 2 (i) (ii) Use, L = 4 m Use, w = 5 kN/m
Problem 2: Cantilever beam In class we derived the spring constant of a beam of length L and constant bending stiffness El clamped at x=0 and subject to a vertical force Fat x= L. Let's study a few different variations of that problem. Let's replace the vertical force F by a counter clockwise bending moement Mo applied at x = L. Recom- pute the equivalent spring constant. Note that in the class we computed spring constant with force and displacement....
Consider the function f(1) = el defined on the interval (0,1). Compute the 2nd order Taylor series approximation to f. Next, compute the approximation to f using the orthogonal projection onto the span of (1,1,2²}, with the inner product of two functions on [0,1] being defined by (5.9) = ['s(a)g(z) ds.
Consider the function f(1) = el defined on the interval (0,1). Compute the 2nd order Taylor series approximation to f. Next, compute the approximation to f using the orthogonal projection onto the span of (1,1,2²}, with the inner product of two functions on [0,1] being defined by (5.9) = ['s(a)g(z) ds.