Question

A weight is suspended from a spring and allowed to hang at its rest posistion. it is then pulled down 2 in.,released, and allowed to oscillate up and down. its location (in inches) relative to its rest posistion is given by the function f(t)=2sin(2.5t-pie/2), where t is the time in seconds.how much time will it take for the weight to move through one complete cycle of motion?
1 )2.5 sec

2)3.1sec

3)3.8sec

4)5.0sec

Answer 1

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 $f(t) = 2\sin (2.5t - \frac{\pi }{2})$, 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, $- 2 = 2 \sin (2.5t - \frac{\pi }{2})$

⇒ $\sin (2.5t - \frac{\pi }{2}) = - 1$

⇒ $(2.5t - \frac{\pi }{2}) = \frac{3\pi }{2}$

⇒ 2.5t = 2π

⇒ t = 2.5 seconds (Approximate)

Therefore, the weight will complete a full cycle in 2.5 seconds. (Answer)