We can get it easily get it from the options.....

All the options have the term a-b

from equations of motion we come to know that as time increases the acceleration decreases and so b decreases..

that is why in the first second a is the longest displacement and hence it is the amplitude.....

the 2a^3 term can be found out using the formulas

v=w(a^2-x^2)^1/2 and the equations of motion..

answer is c 2a^2/3a-b

take the equation of shm of the particle as x = A Cos wt-kx

now apply the given condition for the displacemen in first second

for diplacement in second second find total displacement in 2 secods and subtract it from the displacement in first second.

now, solve the obtained equations..........

u will get the answer yourself................

did u get it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!