Answer:
Step-by-step explanation:
Given that:
mass m = 100 g = 0.1 kg
Length of the spring = 5 cm = 0.05 m
The set in motion from the equilibrium position u(0) = 0
The set in motion from its equilibrium position with a downward velocity u'(0) = 50 cm/s = 0.5 m/s
The spring constant (k) = 
The equation of the system is expressed as:

By estimating the characteristics equation, we have r = ± 14
Thus; the general solution is:

By applying the initial condition:
u(0) = 0
⇒ 0 =
∴

u'(0) = 0.5
0.5 = 14 × c₂
c₂ = 0.5/14
c₂ = 1/28
∴

Equating u(t) = 0, we have t = π/14sec as the time when the mass first returns to its equilibrium position.