The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
$x = \frac{1}{2},\,y = \frac{1}{2}$
$x = - \frac{1}{2},\,y = - \frac{1}{2}$
$x = \frac{1}{2},\,y = - \frac{1}{2}$
$x = - \frac{1}{2},\,y = \frac{1}{2}$
The frequency of vibration $f$ of a mass $m$ suspended from a spring of spring constant $K$ is given by a relation of this type $f = C\,{m^x}{K^y}$; where $C$ is a dimensionless quantity. The value of $x$ and $y$ are
By putting the dimensions of each quantity both the sides we get $[{T^{ - 1}}] = {[M]^x}{[M{T^{ - 2}}]^y}$
Now comparing the dimensions of quantities in both sides we get $x + y = 0\;{\rm{and }}\,2y = 1$
$\therefore $ $x = - \frac{1}{2},\,\,y = \frac{1}{2}$