A particle executing SHM has a velocity of 2 `ms^(-1)` when its displacement from mean position is 1 cm and a velocity of `1 ms^(-1)` when its displacement is 2 cm. Its amplitude of oscillationis

Options

A. 5 cm
B. `sqrt(5) cm`
C. 3 cm
D. `sqrt(7) cm`

Answer

B

Explanation

`(V_(1))/(V_(2))=sqrt((A^(2)-y_(1)^(2))/(A^(2)-y_(2)^(2))),(2)/(1)=sqrt((A^(2)-1)/(A^(2)-2^(2)))`
`4A^(2)-16=A^(2)-1`
`3A^(2)=15,A^(2)=5`
`A=sqrt((2^(2)xx2^(2)-1^(2)xx1^(2))/(2^(2)-1))`
`=sqrt((15)/(3))=sqrt(5)`
By shortcut method, `A=sqrt(v_(1)^(2)+v_(2)^(2))`