Problem 2. At the figure below you see a group of 2 springs - C, and C2. Write the formula for the overall spring stiffness C₂ and calculate the displacement of the springs if F-500 N, C, 300 N/mm, C₂ = 250 N/mm. 100 ½ F 1½ F s C₂
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- In the graph the force versus displacement of a spring is given (the spring is shown in a separate figure--see below). The x-axis range is ±2 cm. The y-axis range is tFs, where Fs = 220 N. How much work does the spring do on the block (the mass "m") when the block moves from x₁ = 7.6 cm to 4.3 cm? W J y F. X -1.5 -0.5 0 10.5 1 1.5 -F How much work does the spring do on the block (the mass "m") when the block moves from x; = 7.6 cm to -7.6 cm? W = Question Help: Read Submit Question mk, k3 A В k2 What is the equivalent spring stiffness between the points A and B. If ki = 1 N/m, k2 =1 N/m. k3 = 2 N/m and k4 = 2 N/m A N/mConsidering the figure shown, determine the equivalent spring constant of a spring that will represent all of the given springs such that its deflection is along a vertical path with the mass. k1=1N/m k2=2N/m k3=3N/m k4=4N/m and k5=5N/m. (answer in N/m) * k2 m k3 k5 k4
- Consider the following spring system. Assume down is the positive direction. Write the stiffness mirix K- • Compute the displacements caused by the external forces f = - Displacement = C₂ m mi heees3 m₂ Hom 3 7/////// with spring constants c = 134Find the equivalent torsional spring constant (up to two decimal points) of the system shown in the figure. Given : R = 0.2 m k1=1 kN.m/rad, k2 = 2 kN.m/rad , k3 = 3 kN.m/rad , k4 = 4 kN.m/rad , k5 = 5kN/m and k6 = 3.0 kN/mFigure below shows two pendulums suspended from frictionless pivots and connected at their midpoints by a spring. Assume that each pendulum can be represented by a mass M at the end of a massless bar of length L. Also assume that the displacement is small and linear approximations can be used for sin 0 and cos 0. The spring located in the middle of the bars is unstretched when 0, = 02. The input force is represented by f (t), which influences the left-hand bar only. Obtain the equations of motion and sketch a block diagram for them.
- Consider the following spring system. 41 with spring constants c = 4 C2 4 Assume down is the positive direction. Write the stiffness matrix K = -24 Compute the displacements caused by the external forces f = 16 Displacement =The first figure gives spring force Fx versus position x for the spring-block arrangement of the second figure. The scale is set by Fs = 190 N. We release the block at x = 13.0 cm. How much work does the spring do on the block when the block moves from x; = +9.0 cm to (a) x = +5.0 cm, (b) x = -5.0 cm, (c) x = -9.0 cm, and (d) x = -11.0 cm? -x (cm) -2 -1 -F, X* = 0 Block attached to spring F = 0 (a) x positive F, negative F (b) x negative F, positive (c)A helical spring is made of 10 m diameter steel wire wound on a 100 mm diameter mandrel. If there are 10 active coils what is spring constant Take: C= 100 GPA What force must be applied to the spring to elongate it by 50 mm?
- As seen in the figure, the block on an inclined plane is lifting from 0 0 with two degrees increment in each step. (0, = 0, 0 =2, 02 = 4, ..) Until which degree can we increase the angle without any slipping between the block and the inclined plane? For condition of F > F, the block continues to hang on the inclined plane. Otherwise, it starts to slip. F, = W + sin8(rad), Fy = W+ cosa(rad) F = F, + u, u = 0.50, W = 100 NA wagon weighing 5100 Kg moving at a speed of 8 km/h has to be brought to rest. Springs made of wire diameter 25mm with a Dm of 250mm and with 24 turns are available. Find the number of springs required in buffer to stop the wagon at a compression of 180mm. b)A close coiled helical spring is made of diameter wire 25mm. The spring index is 8. Findthe number of turns required and maximum allowable load if the allowable shear stress is100 MPa and elongation is limited to 40mm. [G=80 GPa1. Draw the diagram, wrong diagram is wrong. Find the equivalent spring constants if: k1= 100 lb/in k2=200 lb/in k3=100 Ib/in k4=200 lb/in a) k1,k2,k3, and k4 are in parallel b) k1,k2,k3, and k4 are in series c) k1 and k2 are in parallel d) k3 and k4 are in parallel e) k1, k2,k3 are in parallel f) k equivalent in e is in series with k4 g) k2,k3, and k4 are in parallel h) k1 and k equivalent in g are in series