Question

the equation of motion of an object is X=2.0 cos(0.50t+π/4) meters.Its maximum acceleration is?​

Answer 1

answer : maximum acceleration is 0.5 m/s²

explanation : standard equation of particle executing simple harmonic motion is given by,

$x=Acos(\omega t+\phi)$

where A is amplitude, $\omega$ is angular frequency and $\phi$ is phase difference.

comparing both equations,

we get, A = 2m , $\omega$ = 0.5 rad/s

we know, maximum acceleration of particle is $a=\omega^2A$

= (0.5)² × 2 m/s²

= 0.5 m/s²

hence, answer is 0.5 m/s²