Concept explainers
Motion of a Building A strong gust of wind strikes a tall building, causing it to sway back and forth in damped harmonic motion. The frequency of the oscillation is 0.5 cycle per second, and the damping constant is c = 0.9. Find an equation that describes the motion of the building. (Assume that k = 1, and take t = 0 to be the instant when the gust of wind strikes the building.)
The equation which models the motion of the building.
Answer to Problem 45E
The equation for the motion of the building is
Explanation of Solution
Given:
The frequency of the oscillation is
Definition used:
The equation for the damped harmonic motion which describes the displacement y of an object at time t is,
Calculation:
Calculate the equation for the motion of the building at the instant when gust of wind strikes the building,
Assume
The formula to calculate the value of
Substitute the value
The value of
Substitute the value 1 for k,
Therefore, the function for the displacement is
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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