Question

A student was asked to write the equation for displacement at any instant in a simple harmonic motion of amplitude a .He wrote the equation as...

Answer 1

\[y=a \sin [(2\pi v)/k]\times t\]
where v is the velocity at the instant t .For the equation to be dimensionally correct,what should be the dimension of k ?

Answer 2

angles dont have dimensions i want to make 2*pi*v/k*t as a whole dimensionaless
so mke the dimesions cancel out
v is frequency having dimension T^-1
so k is dimensionless constant