Oscillations - springs Two springs, each with unstretched length 0.200 m, but wi

Question

Oscillations - springs Two springs, each with unstretched length 0.200 m, but with different force constants k1 and k2, are attached to opposite ends of a block with mass m on a level, frictionless surface. The outer ends of the springs are now attached to two pins P1 and P2, 0.100 m from the original positions of the ends of the springs (the figure ). Let k1 = 2.50 N/m, k2 = 6.40 N/m, and m = 0.200 kg. Find the length of each spring when the block is in its new equilibrium position after the springs have been attached to the pins.

Explanation / Answer

in the process of fastening the springs to pin p1 and p2 the springs are enlarged to a distance of 0.1mts as the spring constants are different for each springs the forces acting on the block are different so block moves towards the higher force direction to attain equilibrium the work done by both the forces must be equal to conserve energy of the system solving the equations of energy conservation for the situation we can get it making initial block position as reference paint 1/2k1x1^2 +1/2k1x^2 =1/2k2(x1)^2 - 1/2k2x^2 we can get the answer thank u

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