A particle starts SHM from the mean position. Its amplitude is a and total energy E. At one instant its kinetic energy is ` 3( E)/(4)` Its displacement at that instant is:

Options

A. ` ( a) /( sqrt2)`
B. ` (a)/(2)`
C. ` (a)/(sqrt(((3)/(2)))`
D. ` (a)/(sqrt3)`

Answer

B

Explanation

`k = (1)/(2) m omega ^(2) (a^(2) -y^(2)) `
` " " (3)/(4) E = (1)/(2) m omega ^(2) (a^(2) - y^(2)) `
` (3)/(4) ((1)/(2) m omega ^(2) a^(2)) = (1)/(2) m omega ^(2) (a^(2) - y^(2))`
` y^(2) = a^(2) - (3)/(4) a^(2)`
` = (a^(2))/(4)`
` rArr " " y= (a)/(2)`