Question

how k=mw2 where,w=omega[angular frequency]

Answer 1

k = mω2 comes from the solution of the differential equation of SHM obtained from the equation F = -kx. Solution of the SHM differential equation, which is a second order linear ODE is not there in the XI syllabus.

Answer 2

we know ,
F = ma

according to SHM
a = -w²x
put this in above equation ,

F = -mw²x -------(1)

we know ,
spring force
F = -Kx--------(2)

campare equations (1) and (2)

K = mw²