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 of the form

y = ke ctsin (wt)

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. Assume y begins increasing at t = 0.)

Question

Mathematics

Jayden Higgins

29 April, 18:10

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 of the form

y = ke ctsin (wt)

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. Assume y begins increasing at t = 0.)

+3

Answers (1)

Know the Answer?

Cordell Costa · Answer 1

y (t) = e^ (-0.9t) sin πt

Step-by-step explanation:

We are given;

Frequency; f = 0.5 cycles/s

Damping constant; c = 0.9

K = 1

Now relationship between frequency and angular velocity is;

f = ω / (2π)

So, 0.5 = ω / (2π)

ω = 0.5 x 2π

ω = π

So, we want to use the expression;

y (t) = ke^ (-ct) sin ωt

Plugging in the relevant values, we have;

y (t) = 1•e^ (-0.9t) sin πt

y (t) = e^ (-0.9t) sin πt