Grade 11 math  HELP!
posted by Allison on .
Skyscrapers sway in highwind conditions. in one case, at t=2s, the top floor swayed 30cm to the left (30cm), and at t=12, the top floor swayed 30 cm to the right (+30cm) of its starting position.
a) what is the equation of a sinusoidal function that describes the motion of the building in terms of time?
b) if a damper is added to this building, it will reduce the sway (not the period) by 70%. what is the equation of the new function that describes the motion of the building in terms of time?

I assume that the building goes directly from one extreme to the other in 122=10 seconds. Therefore the halfperiod is 10 seconds, or the period T=20 s.
The neutral position is at (2+10)/2=6 seconds, when the displacement is zero.
Thus we have
Xo=30 cm = 0.3m
X(t)=Xo sin((t6)*2π/T), or
X(t)=0.3sin((t6)π/10) 
a) a= 30 cm
1/2 period = 10
period = 20
k= 360/ period
= 360/20
= 18
p = 2
a = 30 (as a reflected cosine)
therefore, d(t)= 30 cos{18(t2)}
b) Reduce sway = reduce of amplitude
a= 100%  70%
= 30%
a = 30 (.3)
= 9 cos{ 18(t2)}