Hello Student,

For a particle executing SHM , it's acceleration can be expressed in the form -------- a = -ω²x or d²x/dt² = -ω²x

According to the question :

d²x/dt² = 16π²x = ω²x

from here we can find out ω which is 4 π

So Time Period = 2 π/ ω = 2 π/4 π = 0.5 sec is the answer.