Answer:
T = 2.82π s
x = Acos(0.71t)
Explanation:
This problem can be solved by using the expressions
[tex]T = 2\pi \sqrt{\frac{m}{k} }[/tex] ( 1 )
[tex]x=Acos(\omega t) = Acos(\frac{2\pi }{T}t )[/tex] ( 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):
[tex]T=2\pi \sqrt{\frac{16 lb}{8lb/ft}} = 2.82\pi s[/tex]
Taking 6 inches as the amplitude of the motion, we have
[tex]x=6cos(\frac{2\pi }{2.82\pi }t ) = 6cos(0.71t)[/tex]
I hope this is useful for you
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