CBSE Class 12-science Answered

if x=asin(pt) and y=bcos(pt) , find the value of d^y/dx^2 at t=0

Asked by Adeeb Khan | 15 Jul, 2014, 01:23: AM

Expert Answer

$x equals a sin space left parenthesis p t right parenthesis y equals b cos space left parenthesis p t right parenthesis A s space t h e r e space i s space n o space d e t a i l s space g i v e n space o n space c o n s tan t s space a comma space b space a n d space p space l e t s space a s s u m e space a comma space b comma space p space a r e space c o n s tan t s fraction numerator d squared y over denominator d x squared end fraction equals fraction numerator d open parentheses begin display style fraction numerator d y over denominator d x end fraction end style close parentheses over denominator d x end fraction equals fraction numerator d open parentheses begin display style fraction numerator begin display style fraction numerator d y over denominator d t end fraction end style over denominator begin display style fraction numerator d x over denominator d t end fraction end style end fraction end style close parentheses over denominator d x end fraction fraction numerator d y over denominator d t end fraction equals minus b p sin space left parenthesis p t right parenthesis fraction numerator d x over denominator d t end fraction equals a p cos space left parenthesis p t right parenthesis fraction numerator begin display style fraction numerator d y over denominator d t end fraction end style over denominator begin display style fraction numerator d x over denominator d t end fraction end style end fraction equals fraction numerator minus b over denominator a end fraction tan space left parenthesis p t right parenthesis fraction numerator d open parentheses begin display style fraction numerator begin display style fraction numerator d y over denominator d t end fraction end style over denominator begin display style fraction numerator d x over denominator d t end fraction end style end fraction end style close parentheses over denominator d x end fraction equals fraction numerator d open parentheses fraction numerator minus b over denominator a end fraction tan space left parenthesis p t right parenthesis close parentheses over denominator d x end fraction equals fraction numerator d open parentheses fraction numerator minus b over denominator a end fraction tan space left parenthesis p t right parenthesis close parentheses over denominator d t end fraction cross times fraction numerator d t over denominator d x end fraction equals fraction numerator minus b over denominator a end fraction p open parentheses s e c squared left parenthesis p t right parenthesis close parentheses cross times fraction numerator s e c left parenthesis p t right parenthesis over denominator a p end fraction equals minus b over a squared s e c cubed left parenthesis p t right parenthesis fraction numerator d squared y over denominator d x squared end fraction equals minus b over a squared s e c cubed left parenthesis p t right parenthesis equals fraction numerator minus b over denominator a squared end fraction left parenthesis a t space t equals 0 right parenthesis$