Question

(a) the displacement of a particle is given by `s - a sin (omega t = kx)`, where `t` is in second and `x` is in meter. Find the dimensions of `omega` and `k`.
(b) The velocity of a praticle is given by `v = v_(0) e^(-lambda t)`, where `t` is time. Find the dimensions of `v_(0)` and `lambda`.

Answer 1

(a) `s = a sin (omega t - kx)`
Angles have no dimensions
`(omega t = kx)` is dimensionless ltbr `omega t`is dimensions, `[k] = L^(-1)`
(b) Power of exponential is dimensionsless.
`lambda t` is dimensions, `[lambda] = T^(-1)`
Dimensions of `v_(0) =` Dimensions of `v`, i.e., `LT^(-1)`
`[V_(0)] = LT^(-1)`