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.
