Amass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. initially, the mass is released from rest from a point 4 inches above the equilibrium position. find the equation of motion. (use g = 32 ft/s2 for the acceleration due to gravity.)

When the spring is in the equilibrium we know that force of the spring is equal to the force of gravity. This allows us to find the spring constant k.

When the system is not in equilibrium the force of gravity and force of the spring are not going to be the same. There is going to be a force acting on the weight.

This is the same differential equation we get for the horizontal spring system. The general solution to this equation is:

Where:

So our final equation will be;

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