Question

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.)

Answer 1

y(t) = e^(-0.9t) sin πt

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