document.write( "Question 1197680: Find the trigonometric model for a simple harmonic motion that has initial displacement of 0 at t=0, and amplitude of 5 inches, and a frequency 4/3 cycles per second \n" ); document.write( "
Algebra.Com's Answer #831066 by ikleyn(52788)\"\" \"About 
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\n" ); document.write( "Find the trigonometric model for a simple harmonic motion that has initial displacement of 0
\n" ); document.write( "at t=0, and amplitude of 5 inches, and a frequency 4/3 cycles per second
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document.write( "The frequency is  4/3 per second.  It means that the period is 3/4 of a second.\r\n" );
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document.write( "The problem says NOTHING about the phase shift.\r\n" );
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document.write( "It only says that the initial displacement is 0 (zero).\r\n" );
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document.write( "There are TWO harmonic (sinusoidal) models satisfying the imposed conditions.\r\n" );
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document.write( "One model is  y = \"5%2Asin%28%28%282%2Api%29%2F%28%283%2F4%29%29%29%2At%29%29\" = \"5%2Asin%28%28%288%2Api%29%2F3%29%2At%29%29\".\r\n" );
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document.write( "Another model is y = \"-5%2Asin%28%28%288%2Api%29%2F3%29%2At%29%29\".\r\n" );
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document.write( "Both models have zero displacements at t= 0.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my solution is that there are TWO different models
\n" ); document.write( "(different geometrically and physically) satisfying the imposed conditions.\r
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\n" ); document.write( "\n" ); document.write( "These models are shifted half-period one from the other.\r
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\n" ); document.write( "\n" ); document.write( "@Theo missed one of them.\r
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\n" ); document.write( "\n" ); document.write( "It is, of course, the major intention of this problem for the student to find BOTH harmonics.\r
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\n" ); document.write( "\n" ); document.write( "I would like to add something at the end.\r
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\n" ); document.write( "\n" ); document.write( "        It is good if you have formal knowledge of a subject.\r
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\n" ); document.write( "\n" ); document.write( "        But in many cases it is not enough to solve problems correctly.\r
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\n" ); document.write( "\n" ); document.write( "        In addition to formal knowledge, you should have adequate physical and geometrical intuition,\r
\n" ); document.write( "\n" ); document.write( "        which is the same as common sense.\r
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\n" ); document.write( "\n" ); document.write( "        The problems like this one help you to develop such intuition and common sense. \r
\n" ); document.write( "\n" ); document.write( "        It is the major benefit of solving such problems.\r
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