Simple Harmonic Motion -05- Initial Phase Angle

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The following is a time-lapse graph of a particle in simple harmonic motion. What is its initial phase angle?  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.

Transcript

00:00Hi friends, there is no limit to learning.

00:05The more diligent you are, the more knowledge you will have.

00:11We have a displacement time graph.

00:15Now, we are asked to find the initial phase angle.

00:22As a refresher, consider the following spring ball system.

00:27Both systems have the same amplitude, the same period, and the same frequency.

00:34Why are the motions of the two systems different?

00:39This is the role of the initial phase angle.

00:42That's because the ball was initially displaced from a different point.

00:47So the ball's displacement at the initial time determines the value of the initial phase angle.

00:55Look at the displacement time graph in our problem.

01:00The initial displacement is square root 3 cm, y at 0 seconds is equal to 3 cm.

01:10In addition, we see the amplitude value, a is equal to 2 cm.

01:17Now, write the general equation of simple harmonic motion, y is equal to a sine of omega t plus phi.

01:24If you still remember, the initial deviation angle is measured at the beginning of time.

01:29The value of t is 0.

01:32Y 0 is equal to a sine of phi.

01:38Just substitute the values of a and y 0.

01:43The sine of phi is equal to half the square root of 3.

01:48I think we already know that half the square root of 3 is the value of the sine of 60 degrees.

01:55So phi is equal to 60 degrees.

02:01Is this value really correct?

02:06If we extend the curve to the left, the displacement time graph would be a sine curve.

02:14If so, the initial displacement point is actually in quadrant 2.

02:20The angle phi should be between 90 degrees and 180 degrees.

02:27Besides 60 degrees, 120 degrees also yields a value of half the square root of 3.

02:35This is the answer to this question, phi equals 120 degrees.

02:41In radians, that value is 2 thirds pi radians.

02:47Happy learning, everyone!

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