document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197680>Question 1197680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831060 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if you are graphing this using the sine function, i would think the equation would be:<BR>\n" );
document.write( "y = 5 * sin(4/3 * x).<BR>\n" );
document.write( "that would give you an amplitude of 5 inches with a displacement of 0 at x = 0 (x take the place of t in the graph).<BR>\n" );
document.write( "there would be no horizontal or vertical shift.<BR>\n" );
document.write( "the graph would look like this:\r<BR>\n" );
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document.write( "if you used the cosine function, then a horizontal shift would be required.<BR>\n" );
document.write( "i think the equation would then be:<BR>\n" );
document.write( "y = 5 * cos(4/3 * (x - 3pi/8))<BR>\n" );
document.write( "that would give you an amplitude of 5 inches with a displacement of 0 at x = 0 (x take the place of t in the graph).<BR>\n" );
document.write( "there would be no vertical shift, although a horizontal shift of 3pi/8 would be required.<BR>\n" );
document.write( "the graph would look like this:\r<BR>\n" );
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document.write( "the graphs show that you would complete 4 full cycles in what would normall be 3 full cycles.<BR>\n" );
document.write( "that's because the frequency is 4/3 * the  normal frequency, which would be 1.\r<BR>\n" );
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document.write( "the graphs, themselves, would be identical, except for the equations used.\r<BR>\n" );
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document.write( "the initial displacement is 0 in both graphs, and the amplitube is 5 in both graphs.\r<BR>\n" );
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