A particle P of mass m kg is attached to two fixed points A and B by two identic

Question

A particle P of mass m kg is attached to two fixed points A and B by two identical model springs, each of stiffness k and natural length lo. The point A is at a height 1/4lo above the point B. The particle is free to oscillate vertically under gravity. The stiffness of each spring is given by k = 4mg/lo. The horizontal level passing through the fixed point A is taken as the datum for the gravitational potential energy. The particle P is initially released from rest at a distance lo below A When m = 4.54 kg and lo = 4.59 m, calculate the total mechanical energy (can be either positive or negative) of the system, in joules. Give your answer to 3 decimal places and take g = 9.81 ms-2.

Explanation / Answer

total mechanical energy=-mgx+0.5k(x1^2+x2^2) x1 and x2 are spring expansions/contraction os left and right spring respectively E=-4.54*9.81*4.59+0.5*4*4.54*9.81/4.59*(0+(3/4*4.59)^2) =25.5533 J

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