Question

A tall building is swaying back and forth on a gusty day. The wind picks up and doubles the amplitude of the oscillation. By what factor does the maximum speed of the top of the building increase? The maximum acceleration?

Answer 1

The maximum speed increased by 2.

The maximum acceleration increased by 2

Explanation: The tall building can be seen as a simple harmonic motion(SHM).

The equation for SHM is given as

X=Asin wt

Where A is the amplitude

W is the angular frequency.

Since it is a simple harmonic motion, the frequency does not change.

Speed/ velocity is given by the equation

V=we

Since r has doubled,speed has doubled.

The equation for acceleration is given as:

a=W^2r

Acceleration has doubled since r has doubled