Answer:
a.) L = 2.64 kgm^2/s
b.) V = 4.4 m/s
Explanation: Jessica stretches her arms out 0.60 m from the center of her body. This will be considered as radius.
So,
Radius r = 0.6 m
Mass M = 2 kg
Velocity V = 1.1 m/s
Angular momentum L can be expressed as;
L = MVr
Substitute all the parameters into the formula
L = 2 × 1.1 × 0.6 = 1.32kgm^2s^-1
the combined angular momentum of the masses will be 2 × 1.32 = 2.64 kgm^2s-1
b. If she pulls her arms into 0.15 m,
New radius = 0.15 m
Using the same formula again
L = 2( MVr)
2.64 = 2( 2 × V × 0.15 )
1.32 = 0.3 V
V = 1.32/0.3
V = 4.4 m/s
Her new linear speed will be 4.4 m/s
We have that the spring constant is mathematically given as

Generally, the equation for angular velocity is mathematically given by

Where
k=spring constant
And

Therefore

Hence giving spring constant k

Generally
Mass of earth 
Period for on complete resolution of Earth around the Sun


Therefore


In conclusion
The effective spring constant of this simple harmonic motion is

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"This resolving power" was obviously stated earlier, somewhere before the point where you started copying. With no resolving power specified, there's actually no question, and so no answer.
The formula for average speed is

So we can just substitute our data.

- its the result