The displacement of an oscillating particle is given by $y=A\sin (Bx+Ct+D)$. The dimensional formula for (ABCD) is

Displacement,

$\mid y=A\sin (Bx+Ct+D)$

$A=y=\left[\mathrm{L}\right]$

As each term inside the brackets is dimensionless, so

$B=\frac{1}{x}=\left[{\mathrm{L}}^{-1}\right]$

$C=\frac{1}{t}=\left[{\mathrm{T}}^{-1}\right]$

and D is dimensionless.

$\therefore \left[ABCD\right]=\left[\mathrm{L}\right]\left[{\mathrm{L}}^{-1}\right]\left[{\mathrm{T}}^{-1}\right]=\left[{\mathrm{M}}^0{ \mathrm{L}}^0{ \mathrm{T}}^{-1}\right]$