Question

Tall buildings are designed to sway in the wind. In a 100 km/h wind, for example, the top of the 110-story Sears Tower oscillates horizontally with an amplitude of 15cm . The building oscillates at its natural frequency, which has a period of 7.0 s.

Assuming SHM, find the maximum horizontal velocity experienced by a Sears employee as she sits working at her desk located on the top floor.

Find the maximum acceleration experienced by a Sears employee as she sits working at her desk located on the top floor.

Compare the maximum acceleration (as a percentage) with the acceleration due to gravity.

*Make sure to include units. Thankyou

Answer 1

In all cases, I assume you mean magnitude, i.e. magnitude of velocity and and magnitude of acceleration.

In simple harmonic motion

ω which is the angular frequency is given by:ω = 2πf

f is the natural frequency and is given by: f = 1/T

T is the period of oscillation.

ω can also be expressed by :ω = 2π/T

The maximum horizontal velocity is:

The maximum horizontal acceleration is:

Comparing this with the acceleration due to gravity:

ofgravity or another way to put it:

Those are your answers.