Question
Tall buildings are flexible and undergo simple harmonic motion (SMH) when excited by wind. Suppose the top floor of a skyscraper is in SMH, swaying back and forth with a frequency of 0.181 Hz and an amplitude of 1.5 m.
a.What is the maximum speed experienced by top floor occupants?
b.What is the maximum acceleration experienced by top floor occupants?
a.What is the maximum speed experienced by top floor occupants?
b.What is the maximum acceleration experienced by top floor occupants?
Answers
Damon
x = 1.5 sin (2 pi * .181 t)
= 1.5 sin (1.137 t)
v = dx/dt = 1.5* 1.137 cos (1.137 t)
v max = 1.5 * 1.137
a = d^2x/dt^2 = -1.5*1.137^2 sin (1.137 t)
a max = 1.5 * 1.137^2
= 1.5 sin (1.137 t)
v = dx/dt = 1.5* 1.137 cos (1.137 t)
v max = 1.5 * 1.137
a = d^2x/dt^2 = -1.5*1.137^2 sin (1.137 t)
a max = 1.5 * 1.137^2