P$6$: A wave packet is constructed at $t=0$ by superposing waves, their wavelengths varying continuously in the following way $y(x,t)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}A(k)cos(kx)dk$

Where $A(k)=$A for $(k_0-\frac{k}{2})k_s(k_0+\frac{k}{2})$ and $=0$ otherwise. Sketch approximately $y(x,t)$ and estimate $x$ by taking the difference between two values of $x$ for which the central maximum and nearest minimum is observed in the envelope. Verify uncerlainty principle from this.