The displacement y of a particle in a medium is given by the...

According to the principle of dimensional homogeneity, the argument of a trigonometric function must be dimensionless.

Therefore, the quantities $bt and cx$ are dimensionless.

$[bt] = [M^0 L^0 T^0] \Rightarrow [b] = \dfrac{1}{[t]} = [T^{-1}]$

$[cx] = [M^0 L^0 T^0] \Rightarrow [c] = \dfrac{1}{[x]} = [L^{-1}]$

The ratio $\dfrac{b}{c}$ has the dimensions:

\left[\dfrac{b}{c}\right] = \dfrac{[T^{-1}]}{[L^{-1}]} = [L T^{-1}]$<br><br>This corresponds to the dimensional formula$[M^0 L T^{-1}]$.<br><br>Answer:$[M^0 L T^{-1}]