The maximum kinetic energy of a mass-spring system in SHM is equal to

Answer 1

(1/2) m Vmax^2

if x = a sin w t
v = a w cos wt
so
Vmax = a w

a is amplitude
w is circular frequency = 2 pi f

so
Ke max = (1/2) m (a^2 w^2)
= 2 pi^2 m a^2 f^2