The phase difference between two SHM ${\mathrm{y}}_1 = 10 \sin (10\mathrm{\pi t} + \frac{\mathrm{\pi }}{3}) \mathrm{and} {\mathrm{y}}_2 = 12 \sin (8\mathrm{\pi t}+\frac{\mathrm{\pi }}{4}) \mathrm{at} \mathrm{t} = 0.5 \mathrm{s} \mathrm{is}$

 

Phase for 1st SHM: $\varnothing = 10\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}$

Phase for 2nd SHM: $\varnothing { }_2 = 8\mathrm{\pi t}+\frac{\mathrm{\pi }}{4}$

Phase difference: $∆\varnothing = {\varnothing }_1-{\varnothing }_2 = 2\mathrm{\pi t} + \frac{\mathrm{\pi }}{12}$

Put t = 0.5 s

$∆\varnothing = 2\mathrm{\pi }(0.5)+\frac{\mathrm{\pi }}{12} = \frac{13\mathrm{\pi }}{12}$