The maximum acceleration of a simple harmonic oscillatore is `a_(0)` and maximum velocity is `v_(0)`. What is the displacement amplitude?

Explanation

Let A be the amplitude and `omega` be the angular frequency of SHM. Then
Maximum velocity, `v_(0)=omegaA or omega=v_(0)//A`
Maximum acceleration,
`a_(0)=omega^(2)A=(v_(0)^(2))/(A^(2))A=(v_(0)^(2))/(A)`
`:.` Amplitude `A=(v_(0)^(2))/(a_(0))`