The maximum velocity and maximum acceleration of a particle per for ming a linear SHM are `alpha and beta` respectively. Then path length of the particle is

Options

A. `(alpha^(2))/(beta)`
B. `(beta)/(2 alpha^(2))`
C. `(2 alpha^(2))/(beta)`
D. `(2 beta)/(alpha^(2))`

Answer

C

Explanation

`alpha = V_(max)=A omega and a_(max)=A omega^(2) = beta`
`therefore" "(alpha^(2))/(beta)=(A^(2)omega^(2))/(Aomega^(2))=A`
`therefore` Path length `= (2 alpha^(2))/(beta)`