Question

k=15, c=0.25, f=0.6 An initial amplitude k, damping constant c, and frequencyf or period p are given. (Recall that frequency and period are related by the equation f=1 / p.) Find a function that models the damped harmonic motion. Use a function of the form y=ke⁻ᶜᵗ cos ωt, and of the form y=k e⁻ᶜᵗ sin ωt

Answer 1

The function that models damped harmonic motion is y = ke^-ctcos(ωt), where k is the initial amplitude, c is the damping constant, t is time, and ω is the angular frequency. You can calculate the angular frequency ω by using the equation f = 1/p, where p is the period. Substitute the given values into the equation to calculate ω and then substitute all the values into the final equation to obtain the function that models the damped harmonic motion.

Step-by-step explanation:

The function that models damped harmonic motion is given by:

y = ke-ctcos(ωt)

where:

• y is the displacement
• k is the initial amplitude
• c is the damping constant
• t is time
• ω is the angular frequency

To find the function that models damped harmonic motion, you are given the values k = 15, c = 0.25, and f = 0.6. To calculate ω, use the equation f = 1/p, where p is the period. Substitute the given values into the equation to calculate ω. Then, substitute the values of k, c, and ω into the function y = ke-ctcos(ωt) to obtain the final function that models the damped harmonic motion.