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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