The equation for the force of a spring is: F = -k*(dx)
k - spring constant
dx - change in elongation of spring
The force of gravity on the ball has to be the same as the force on the spring (when at rest), so
mg = k*(dx) (you can drop the negative sign since you know the forces are in opposite directions)
When you plug in all the numbers, you get k = 19.6 N/m
(pay attention to units... the easiest thing to do is change everything to meters and kilograms)
For the second part, the frequency of the motion is:
T = 2*pi*(m/k)^0.5
You now have both m (mass) and k, so you can plug in and get
T = 0.401 s

The potential energy stored in a spring is given by this formula:
U = 1/2 • k • x^2
Where U is the potential energy, k is the spring constant, and x is the distance that the spring is compressed or stretched. Thus, in this case:
U = 1/2 • k • x^2
U = 1/2 • 100 N/m • (0.2 m)^2
U = 50 N/m • 0.04 m^2
U = 2 Joules
The kinetic energy of the block will be equal to the potential energy of the spring. This happens because all of the energy stored as elastic potential energy in the spring is converted into kinetic energy when the spring is released. Since KE = 1/2 • m • v^2, we know that:
1/2 • m • v^2 = U
m • v^2 = 2U
v^2 = 2U/m
v = SQRT (2U/m)
By substituting m = 0.5 kg and U = 2 Joules, you get:
v = SQRT (4 J / 0.5 kg)
v = SQRT (8 m^2/s^2)
v = 2.828 m/s
So, our final answer is that the potential energy in the spring is 2 Joules, and the velocity of the block is 2.828 m/s. Hope this helps!

a) k(avg)= (k1 + k2)/2
k(avg)= (4+ 6)/2=5 N/m
b) Ps=.5k(avg)X^2 (potential energy of the spring)
Ke=.5mV^2 (kinetic energy of the mass)
Pe=Ke
then
X(max)=sqrt(mV^2/k(avg))
X(max)=sqrt(1.0 (0.5)^2 / 5)
X(max)=0.316 m or 31.6 cm