Simple Harmonic Motion -04- Vibration displacement

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A particle undergoes simple harmonic motion according to the equation y = 1.2 sin (¼πt - ⅙π) cm. What is the particle's displacement 8 seconds later?  watch the related video SIMPLE HARMONIC MOTION: https://dailymotion.com/playlist/x7zqtm  #oscillation #simpleharmonicmotion  By following this channel it is very useful for the development of this channel. The Dailymotion application is easy to install on any smartphone, and does not take up much memory space.

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00:00Hi friends, education isn't everything, but everything starts with education.

00:07The displacement of a particle in simple harmonic motion can be formulated as a sine equation.

00:15In this series, we'll learn how to calculate the displacement at a specific instant.

00:22You might not know what displacement is.

00:28Consider the simple harmonic motion of the spring ball system below.

00:34The ball moves back and forth up and down past the equilibrium point.

00:43The displacement is the distance the ball travels from the equilibrium point.

00:50Suppose the ball reaches this point at a specific instant.

00:56From the equilibrium point, a straight line can be drawn to the center of the ball.

01:01The length of this line is the displacement.

01:06In our problem, the displacement of the ball is written as y equals 1.2 sine of 1 quarter pi t minus 1 sixth pi.

01:17To find the displacement at t equals 8 seconds, simply substitute 8 into the equation.

01:27Most students will have trouble here.

01:30Our minds tell us that pi is 3.14 or 22 over 7.

01:38This is true if pi is not an angle in degrees.

01:44When pi is inside a trigonometric function, it is 180 degrees.

01:51Its value inside a sine is 330 degrees.

01:57The sine of 330 degrees can be written as the sine of 360 minus 30.

02:06Based on the trigonometric identity, this value is minus sine 30 degrees.

02:14I think we all know the value of sine 30.

02:18That is half.

02:21y equals minus 0.6 centimeters.

02:27There is a minus sign there.

02:29This means the ball is 0.6 centimeters below the equilibrium point.

02:36Happy learning everyone!

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