document.write( "Question 1183585: Owen is jumping on a trampoline. When his feet hit the deck of the trampoline, the material depresses to a minimum height of 2cm. On average, Owen is reaching a maximum height of 200cm every 10 seconds. Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.
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Algebra.Com's Answer #813977 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "Owen is jumping on a trampoline. When his feet hit the deck of the trampoline,
\n" ); document.write( "the material depresses to a minimum height of 2cm.
\n" ); document.write( "On average, Owen is reaching a maximum height of 200cm every 10 seconds.
\n" ); document.write( "Determine the equation of a sinusoidal function that would model this situation, assuming Owen reaches his first maximum at 6 seconds.
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\n" ); document.write( "\n" ); document.write( "I will not consider the physical processes described in the post.\r
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\n" ); document.write( "\n" ); document.write( "I will re-formulate Math problem formally.\r
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document.write( "    Restore a sinusoidal function based on following data:\r\n" );
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document.write( "        - the minimum height is 2 cm;  the maximum height is 200 cm;\r\n" );
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document.write( "        - the period is 10 seconds;\r\n" );
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document.write( "        - the body is in its upper position at t= 6 seconds.\r\n" );
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document.write( "The midline is half-way between y= 2 cm and y= 200 cm, so midline is y =  =  = 101 cm.\r\n" );
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document.write( "The amplitude \"a\" is half the distance between the level 2 cm and 200 cm, or  a =  =  = 99 cm.\r\n" );
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document.write( "Since the upper position is at t= 6, I will use the cosine function\r\n" );
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document.write( "    y =  + ,\r\n" );
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document.write( "starting my argument (the chronometer) from 6 seconds,  where T is the period.  \r\n" );
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document.write( "The period value is given as T = 10 seconds, so my final expression for the function is\r\n" );
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document.write( "    y = 101 + .\r\n" );
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document.write( "In this form, the meaning of each term, parameter and value is visible and understood very well.\r\n" );
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document.write( "You can transform my expression further by any EQUIVALENT way, if you need and if you want.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The major things in this analysis is not getting the final expression.\r
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\n" ); document.write( "\n" ); document.write( "The major thing is to understand what to do with the given parameters.\r
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