Question

PLEASE HELP!!!! A weight is attached to a spring that is oscillating up and down. It takes 3 sec. for the spring to complete one cycle, and the distance from the highest to lowest point is 4 in. What equation models the position of the weight at time t seconds?

A. y=2sin(pi/3 t)

B. y=4sin(pi/3 t)

C. y=2sin(2pi/3 t)

D. y=4sin(2pi/3 t)

E. y=2sin(3pit)

F. y=4sin(3pit)

Answer 1

Option C.

Explanation:

The equation that models the position of the weight and time will be a sine wave.

y = A sin(bt)

where A = amplitude of the wave

b = time period for a complete oscillation

Since b =
`(2\pi )/(t)`

It has been given in the question, Time period t = 3 sec.

b =
`(2\pi )/(3)`

Amplitude A = 2 in.

Now we plug in the values of amplitude and time period in the standard equation.

y =
`2sin((2\pi )/(3)* t)`

y =
`2sin((2\pi t)/(3))`

Option C. is the answer.