Answer:
n_cladding = 1.4764
Explanation:
We are told that θ_max = 5 °
Thus;
θ_max + θ_c = 90°
θ_c = 90° - θ_max
θ_c = 90° - 5°
θ_c = 85°
Now, critical angle is given by;
θ_c = sin^(-1) (n_cladding/n_core)
sin θ_c = (n_cladding/n_core)
n_cladding = (n_core) × sin θ_c
Plugging in the relevant values, we have;
n_cladding = 1.482 × sin 85
n_cladding = 1.4764
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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300/8 = 37.5
37.5 x 12 = 450
New temp. = 450 K
Hope this helps!