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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