The displacement of a particle varies according to the relationx = 4(cos πt + sin πt)The amplitude of the particle is

x = 4(cos πt+sin πt)   = 42[12cos πt+12sin πt]  = 42[sinπ4cosπt+cosπ4sinπt]= 42 sin(πt+π4)Standard equation of displacement is:x = a sin (ωt+∅)Comparing the given equation with standard equationa = 42