Posted by **Allison** on Tuesday, December 21, 2010 at 3:29pm.

Skyscrapers sway in high-wind 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?

- Grade 11 math - HELP! -
**MathMate**, Wednesday, December 22, 2010 at 10:04pm
I assume that the building goes directly from one extreme to the other in 12-2=10 seconds. Therefore the half-period 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((t-6)*2π/T), or

X(t)=0.3sin((t-6)π/10)

- Grade 11 math - HELP! -
**yuriy**, Thursday, March 12, 2015 at 3:33pm
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(t-2)}

b) Reduce sway = reduce of amplitude

|a|= 100% - 70%

= 30%

|a| = 30 (.3)

= 9 cos{ 18(t-2)}

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