Define a weakly stationary stochastic process \(\{V(t), t \geq 0\}\) by

\[V(t)=S(t+1)-S(t)\]

where \(\{S(t), t \geq 0\}\) is the standard Brownian motion process.

Prove that its spectral density is proportional to

\[\frac{1-\cos \omega}{\omega^{2}}\]