An object of mass 2 kg is connected to two springs. One end of each spring is co

Question

An object of mass 2 kg is connected to two springs. One end of each spring is connected to the object, and the other is anchored at a point on the x axis. Spring 1 has a compression factor of 8 N/m, uncompressed length of 5 meters, and is anchored to the coordinate x1 = -6 m. Spring 2 has a compression factor of 7 N/m, uncompressed length of 3 meters, and is anchored to the coordinate x2 = 9 m. If the object is released from rest at the origin, what is the speed with which it will pass through the equilibrium point?

The speed with which it will pass through the equilibrium point is m/s.

thank you!!!!!!!!!

Explanation / Answer

8l = 7(7-l)

l = 3.266 m

equilibrium position is at x = -6+5+3.266 = 2.266m

Initial energy = Final energy

0.5*8*1^2 + 0.5*7*6^2 = 0.5*8*(1+2.266)^2 + 0.5*7*(6-2.266)^2 + 0.5mv^2

0.5mv^2 = 38.533

v = 6.207m/s

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