Find a model for simple harmonic motion if the position at t = 0 is 4, the amplitude is 4 centimeters, and the period is 6 seconds.

B. d = 4 cos(π/3 t)

Step-by-step explanation:

As at t=0 the amplitude is 4 cm, so the simple harmonic motion will be in cosine form. As in case of sine function, the value of function at t=0 is 0.  

sin 0=0

We know that,

y = a. cosb(t + c) + d

Period = 2 π / b

Horizontal shift or phase shift is c,

Amplitude is a,

Vertical shift is d.

As in this case the amplitude is given to be 4, hence  = 4

Also the period is given as 6.

That is, 2π/b = 6

b = 2π/6 = π/3

Here horizontal and vertical shifts are 0.

That is c = 0 and d = 0

Plug those values in the above form, we get

y = 4.cos π/3 (t + 0) + 0

y = 4 cos (π/3)t

B. d = 4 cos(π/3 t)

Hope this will helpful.

Thank you.

answer: 12   they all have at least 28 days

step-by-step explanation: haha