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Key variables:

a = a(t)= amplitude

k= initial amp

c= damping constant

omega = h. stretch (or comp.)

Basic Example

#1: k=20, c=0.5, p=4, y=a(t)cos(omega*t)

Answer

Word Problems

Guitar

#2: A guitar string is plucked and vibrates in damped harmonic motion. The string is pulled and displaced 2cm from its resting position. After 3 seconds, the displacement of string measures 1 cm. Find the damping constant.

Ans: ln(2)/3

Animal Population

#3: A deer population oscillates 19 above and below the average during the year, reaching the lowest value in January. The average population starts at 800 deer and increases by 160 deer each year. Find a function that models population, P, in terms of months since January (t).

Ans: P(t)= -19cos([pi/6]t)+800 + 40t/3

Spring

#4 A spring measuring 10 inches in natural length is compressed by 5 inches and released. It oscillates once every 3 seconds and its amplitude decreases by 30% every second. Find an equation that models the position of the spring “t” seconds after geing released.

Ans: y= [-5e^(-0.357t)]cos([2pi/3]t)+10

#5

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Sanjay Kumar Mohindroo Sanjay Kumar Mohindroo. skm.stayingalive.in Did You Know You Could Fall to the Center of the Earth in 19 Minutes If a tunnel ran through the Earth, a free-fall trip to the center would take just 19 minutes. Explore the physics, history, and science of this fascinating concept. The Fascination of Falling Through Earth A Hypothetical Yet Scientific Adventure Have you…

07/03/18

An example of simple harmonic motion used in my game, on an object which will be used as a pickup item of interest.

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EITHER YOU SUCK. OR MY TEACHER SUCKS AT EXPLAINING YOU.