Question

Can someone help with this physics it stressing me out

Answer 1

There's no benefit from being stressed out, my lord.

               x = 8 cos(3t + π/3)

When t=0,        x = 8 cos(π/3)

Position  =  8 cos(π/3) = 8 (0.5)  =  4 .

Speed = first derivative of  8 cos(3t + π/3) =

                 - (8) (3) sin(3t + π/3)  =  - 24 sin(π/3)  =  -20.78

Acceleration = second derivative of    8 cos(3t + π/3)  

                   = first derivative of    - 24 sin(3t + π/3) 

                   =        - (24) (3) cos(3t + π/3)

                   =        -72 cos(π/3)  =  -36  .

The period of the motion is the period of   cos(3t + π/3) .
That's the same as the period of  cos(3t) .
When is the first time after (3t=0) when (3t=2π) ?   It's  t = 2π/3 .
The period is   2π/3  .

The amplitude of the motion is the amplitude of     8 cos(.....) .
The amplitude of the cosine is 1 .
The amplitude of     8cos(...)    is  8 .


Words cannot express my boundless gratitude
for the generous gift of your 5 points, my lord.
A full 1 point per answer !
The warm cloudy water and green bread-crust are delicious too.