A 16 pound weight attached to a spring exhibits simple harmonic motion. Determine the equation of motion if the spring constant is 8 lb/ft and if the weight is released 6 inches below the equilibrium position with a downward velocity of 1 ft/s.

T = 2.82π s

x = Acos(0.71t)

Explanation:

This problem can be solved by using the expressions

   ( 1 )

  ( 2 )

where T is the period of oscillation of the system, m is the mass of the object attached to the spring, k is the spring constant and x is the position of the object.

By replacing in the expression (1):

Taking 6 inches as the amplitude of the motion, we have

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