Question

given that the displacement of an oscillating particle is given by Y is equal to Asin bx + c t + D the dimensional formula of ABCD​

Answer 1

Answer:

[A]=[L] ; [c] = [LT^(-1)] ; [D]= [L] ; [b] =  [L^(-1)]

Explanation:

Given equation $y=Asinbx+ct+D$

Note y is displacement whose dimension is [L].

According to dimensional rule,

Dimension of y = Dimension of Asinbx.

We also know sin(x) or any trigonometric function is dimensionless.

Therefore, Dimension of y = Dimension of A

Implies, [y]=[A]. So, [A]=[L]

As angles are also dimensionless

so, dimension of bx = dimensionless

[bx] = dimensionless Or, [b] = [x ^(-1)] = [L^(-1)]

Also, [y]=[c][t]

or [c]=[y]/[t] = [L] / [T] = [LT^(-1)]

And [y] = [D]

Or [D] = [y] = [L]