Answer:
The weight will complete a full cycle in 2.5 seconds.
Step-by-step explanation:
The weight is pulled down 2 inches, released, and allowed to oscillate up and down.
Now, its location (in inches) relative to its rest position is given by the function [tex]f(t) = 2\sin (2.5t - \frac{\pi }{2})[/tex], where t is the time in seconds.
Now, the initial position of the weight was at f(0) = - 2 inches and again after t seconds, it will reach -2 inches distance to complete a cycle.
Then, [tex]- 2 = 2 \sin (2.5t - \frac{\pi }{2})[/tex]
⇒ [tex]\sin (2.5t - \frac{\pi }{2}) = - 1[/tex]
⇒ [tex](2.5t - \frac{\pi }{2}) = \frac{3\pi }{2}[/tex]
⇒ 2.5t = 2π
⇒ t = 2.5 seconds (Approximate)
Therefore, the weight will complete a full cycle in 2.5 seconds. (Answer)
