An object of mass 9 kg is connected to two springs. One end of each spring is co

Question

An object of mass 9 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 6 N/m, uncompressed length of 2 meters, and is anchored to the coordinate x1 = -9 m. Spring 2 has a compression factor of 8 N/m, uncompressed length of 4 meters, and is anchored to the coordinate x2 = 6 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.

Explanation / Answer

An object of mass 3 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 4 N/m, uncompressed length of 1 meters, and is anchored to the coordinate x1 = -8 m. Spring 2 has a compression factor of 7 N/m, uncompressed length of 2 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?

say 'x' is the coordinate where its at equilibrium

so

7*(x-(-8))=4*(9-x)........Equating both spring forces k1*x1=k2*x2

so x=21/11 m

when put at x=0 the energy stored in springs=0.5*7*7^2 + 0.5*4*7^2=0.5*11*7^2=269.5 joules

at equilibrium energy in springs=0.5*4*(7+ 21/11)^2 +0.5*7*(7-21/11)^2 =249.45 joules

the difference id the kinetic energy of the mass

so 0.5*3*v^2=20.045 joules

so velocity=3.6556 m/sec

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