The first thing to do is to find the spring constant, k. Hook's law is used to do this: F = -k x. Take the positive
direction of displacements to be downward. So the spring exerts an upward force
of magnitude k 0.1 This balances the downward force of gravity the
magnitude of which is 5 g (g = 9.81). Setting these magnitudes equal (the force balance)
gives k = 5 (9.81)/0.1 = 490.5 N/m.
Next is the analysis of the SHM. the angular frequency, ω , is given by ω =sqrt(k/m)
This evaluates to 9.90 radian/s. The linear frequency, f, is ω/ (2 π) = 1.57 cycles/s.
The period, T, is T = 1/f = 0.634 s.
The amplitude is simply the additional downward displacement = 0.05 m.