Simple Harmonic Motion -06- Displacement-Time Graph

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Draw a sketch of the displacement-time graph of a particle performing simple harmonic motion, y equals 1.8 sin (⅓πt - ⅛π)?  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, learning isn't just about learning facts.

00:05It's about training your mind to think.

00:09We have an equation for a particle performing simple harmonic motion.

00:15Now, we're asked to sketch a displacement time graph.

00:23I think this is quite easy.

00:26Anyway, let's prepare a scaled paper.

00:30A displacement time graph contains two physical quantities, particle displacement and instantaneous time.

00:38Typically, the horizontal axis is time, and the vertical axis is displacement.

00:46Now, write the mathematical equation as shown on the worksheet.

00:53The easiest way is to determine the maximum displacement, or amplitude.

00:59Amplitude is the maximum value of the displacement.

01:02Since the maximum value of the sine is 1, 1.8 is the amplitude value.

01:11This point is 1.8, and this point is minus 1.8.

01:18Next, draw a horizontal dotted line through these two points.

01:25The sine curve must lie between these two dotted lines.

01:30This is the standard sine curve.

01:35In our problem, the initial phase angle is minus one-eighth of pi.

01:41Since pi is 180 degrees inside an angle, the initial phase angle is minus 22.5 degrees.

01:52That's an angle in quadrant 4.

01:56So, we need to shift the sine curve 22.5 degrees to the right to bring the initial displacement into quadrant 4.

02:06For the sketch, we don't need to know the exact value of the initial displacement point.

02:11What is certain is that the particle starts moving from a point below the equilibrium point.

02:19This question only asks for a sketch, the shape of this sine curve seems to be representative.

02:26If you have time to do the detailed calculations, this point is minus 0.7 centimeters.

02:35This point is 0.375 seconds.

02:41The period of simple harmonic motion is 6 seconds.

02:47So this point is 3.375 seconds, and this point is 6.375 seconds.

02:56Happy learning, everyone!

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