document.write( "Question 1179522: I need help with this!!!\r
\n" ); document.write( "\n" ); document.write( "A spring oscillates with a frequency of 8 cycles per second. Its initial displacement is 9 centimeters and it's damping factor is 0.3. Give the function, f(t) that describes the position of the spring t seconds after it starts oscillating. \n" ); document.write( "
Algebra.Com's Answer #809107 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Could you,  or your professor,  or your textbook,  or your other source  EXPLAIN  what they mean saying  \"the damping factor\" ?\r
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\n" ); document.write( "\n" ); document.write( "I am asking,  because different sources give different definitions  (or do not give any definitions,  at all).\r
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\n" ); document.write( "\n" ); document.write( "It looks like,  that every school / college / university / (working group) / company has and uses their own definition of this term.\r
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\n" ); document.write( "\n" ); document.write( "After intensive search in the Internet,  I finally found an adequate definition of the  \"damping factor\"  under this link\r
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\n" ); document.write( "\n" ); document.write( "https://openstax.org/books/precalculus/pages/7-6-modeling-with-trigonometric-equations\r
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\n" ); document.write( "\n" ); document.write( "and now I am ready to present my solution.\r
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document.write( "Had damping be zero, the equation of harmonic oscillations would be\r\n" );
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document.write( "    x(t) = \"9%2Acos%28%282pi%2F8%29t%29\".\r\n" );
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document.write( "\"9\" is the initial displacement; cosine is used due to given initial displacement at the starting moment;  \r\n" );
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document.write( "the argument  \"%282pi%2F8%29%2At\"  accounts for the frequency;  t is the time in seconds after the start.\r\n" );
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document.write( "Since the dumping 0.3 is imposed, the final formula takes the form\r\n" );
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document.write( "    x(t) = \"9e%5E%28-0.3t%29%2Acos%28%282pi%2F8%29t%29\".      ANSWER\r\n" );
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document.write( "x(t) is the position coordinate in centimeters relative to the equilibrium.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved,  answered and explained.\r
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\n" ); document.write( "\n" ); document.write( "Do not forget to post your  \"THANKS\"  to me for my teaching.\r
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\n" ); document.write( "\n" ); document.write( "From your comments, I noticed that you are familiar with the computer system SASSY.\r
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\n" ); document.write( "\n" ); document.write( "Where and how did you get familiarity with it ?\r
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\n" ); document.write( "\n" ); document.write( "I worked several years with this system on different engineering projects . . . \r
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\n" ); document.write( "\n" ); document.write( "And even participated in creating the Manual on this system, after all . . . \r
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