document.write( "Question 856987: A spring with a mass 2kg length 0.5m. A force of 25.6 N is required to maintain its stretched to length of 0.7m. If tie spring stretched to a length of 0.7m and then released with initial velocity 0. Find composition of the mass at any time(t) can be written as acosxt +bsinxt.find the value of a,b,x. \n" ); document.write( "

Algebra.Com's Answer #516303 by Fombitz(32388) $\"\"$ $\"About$

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$\"m=2\"$
\n" ); document.write( " $\"L=0.5\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"F=kx\"$
\n" ); document.write( " $\"25.6=k%280.7%29\"$
\n" ); document.write( " $\"k=36.57\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"y=a%2Acos%28xt%29%2Bb%2Asin%28xt%29\"$
\n" ); document.write( "When $\"t=0\"$ , $\"y=0.7\"$ ,
\n" ); document.write( " $\"0.7=a%2A1%2Bb%2A0\"$
\n" ); document.write( " $\"a=0.7\"$
\n" ); document.write( "When $\"t=0\"$ , $\"dy%2Fdt=0\"$
\n" ); document.write( " $\"dy%2Fdt=-xa%2Asin%28xt%29%2Bxbcos%28xt%29=0\"$
\n" ); document.write( " $\"-xa%2A0%2Bxb%2A1=0\"$
\n" ); document.write( " $\"b=0\"$
\n" ); document.write( " $\"y=0.7cos%28xt%29\"$
\n" ); document.write( " $\"x=sqrt%28k%2Fm%29\"$
\n" ); document.write( " $\"x=sqrt%2836.57%2F2%29\"$
\n" ); document.write( " $\"x=sqrt%2818.286%29\"$
\n" ); document.write( " $\"x=4.28\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"highlight%28y=0.7cos%284.28t%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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