Skyscrapers sway in high wind conditions. In one case, at t = 2s, the top floor of the building swayed as far as 30 cm to the left (-30 cm) and at t = 12s, the top floor swayed as far as 30 cm to the right (+30 cm) from its starting position.
a) What is the equation of a sinusoidal function that describes the motion of the building in terms of time? (I only need help on determining the period and horizontal shift)

Question

Skyscrapers sway in high wind conditions. In one case, at t = 2s, the top floor of the building swayed as far as 30 cm to the left (-30 cm) and at t = 12s, the top floor swayed as far as 30 cm to the right (+30 cm) from its starting position.
a) What is the equation of a sinusoidal function that describes the motion of the building in terms of time? (I only need help on determining the period and horizontal shift)

sanoofy · Answer

@jagr2713

mathmale · Answer

Let x represent the horizontal distance (from some central point) that the top floor of this building reaches as it sways.  Doing this should tell you right away what the amplitude of this sinusoidal function is.  Try graphing this function.  At which time value t would this amplitude be -30 cm?  +30 cm?  

From -30 cm to the left to 30 cm to the right constitutes 1/2 of a full cycle.  Use this fact to determine the period. 

There is no horiz. shift here.  x=0 is the central, or starting, point.