Question

if the displacement of y of aparticle is y=Asin(pt+qx) then dimensional formula of ap is​

Answer 1

given,

If the displacement of y of a particle is y = Asin(pt + qx).

To find,

The dimensional formula of Ap.

we know, equation of displacement of particle performing simple harmonic motion is given by, y = Asin(ωt + kx).

where A is amplitude. so dimensional formula of A = [L]

ω is angular frequency. so dimension formula of ω = [T¯¹]

and k is wave number. so dimensional formula of k = [L¯¹]

on comparing we get,

A = [L]

p = ω = [T¯¹]

and q = k = [L¯¹].

now dimensional formula of Ap = [L][T¯¹] = [LT¯¹]