A mass oscillate with SHM of amplitude A and period T y = A cos (2πt/T). The kinetic energy of the mass is equal with
twice the potential energy of the spring at :
y=Acos(2πt/T)
KE= (mA²ω²/2)sin²(2πt/T)
PE=(mA²ω²/2)cos²(2πt/T)
KE=2PE =>
(mA²ω²/2)sin²(2πt/T) = 2 (mA²ω²/2)cos²(2πt/T)
tan²(2πt/T)=2
tan (2πt/T)=√2 =1.41
(2πt/T) = arctan 1.41 = 0.954 rad
t= 0.954T/2π = 0.15T