A mass weighing 64lb is attached to a spring hanging from the ceiling and comes to rest at its equilibrium position. At time t=0
, an external force of F(t)=3cos4t lb is applied to the system. If the spring constant is 20 lb/ft and the damping constant is 2 lb-sec/ft, find the steady-state solution for the system. Use g=32 ft/sec^2
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Answer:
Step-by-step explanation:
Completing the square is a process of converting a quadratic equation in standard form into vertex form.
The first step in completing the square is grouping the quadratic and linear terms of the quadratic equation.
Factor out the coefficient of the quadratic term,
Now complete the square, add a term to make the grouped part of the equation a complete square, then balance the equation.
Simplify,
The x-coordinate of the vertex of the equation is equal to (-1) times the numerical part of the quadratic term, and the y-coordinate is equal to the constant.