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Differential Equations: Motion of a Spring

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First published at 08:29 UTC on October 27th, 2018.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I go over further into differential equations and this time use Hooke's Law to establish a relationship between the resistance force of a spring as being proportional to the length it stregths (or compresses). Since we are dealing with a force, we can apply Newton's Second Law of motion, which states that a force is equal to its mass times its acceleration. The acceleration of an object can also be considered as the second derivative of position of the spring. Thus we can model the motion of a spring through a second-order differential equation. It is called second-order because of it involves a function and its second derivatives.

Functions that fit this description are the sine and cosine functions, since the second derivatives both are themselves but with a negative sign. And similar to trigonometric functions, the motion of a spring oscillates which makes trig functions reasonable solutions to the motion of a spring differential equation.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsEgtmClosN58R6igg

Related Videos:

Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Integrals and Work: Example 2 - Hooke's Law: http://youtu.be/h8lwvB9rOng
Higher Derivatives Example on Acceleration: http://youtu.be/PVxUQjJ1vUA .

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