Question

Derive by the method of dimensions, an expression for the energy of a body executing simple harmonic motion, if it depends upon the mass 'm', the frequency 'f' and the amplitude of vibration 'r' of the body.

Answer 1

Dear Student,
E= k m^af^br^c
Where E = Energy of pendulum., m = mass, f= frequncy, r= amplitude of vibration, k= constant
Using Dimensions ,

M¹L²T^-2=k M^aT^-bL^c

Thus , a=1, b=2, & c=2

So, E=k m f² r².