Question

An initial amplitude k ,damping constant c ,and frequency f or period p are given. (Recall that frequency and period are related by the equation f=1/p.) k=2, c=1.5, f=3 Find a function that models the damped harmonic motion. Use a function of the form y=ke⁻ᶜᵗ cos (ωt)

Answer 1

To model the damped harmonic motion, we can use the function y = ke^-ctcos(ωt), where k is the initial amplitude, c is the damping constant, and ω is the angular frequency.

Step-by-step explanation:

To model the damped harmonic motion, we can use the function y = ke-ctcos(ωt), where k is the initial amplitude, c is the damping constant, and ω is the angular frequency.

In this case, k = 2, c = 1.5, and f = 3. Since frequency and period are related by f = 1/p, we can find the period as p = 1/f = 1/3.

Therefore, the function that models the damped harmonic motion is y = 2e-1.5tcos(6πt).