This question was previously asked in

BPSC Asstt. Prof. ME Held on Nov 2015 (Advt. 22/2014)

Option 2 : less than ω_{n}

ISRO Scientist ME 2020 Paper

1464

80 Questions
240 Marks
90 Mins

**Concept:**

**Effective mass** will come into the picture if we will consider the mass of the beam.

For the case of a simply supported beam

Effective mass and effective stiffness is given by:

\({M_{eff}} = M + \frac{{68m}}{{140}}\) and \({K_{eff}} = \frac{{48EI}}{{{L^3}}}\)

where m is mass of the beam and M is mass placed on the beam

From here we can see that while considering the mass of the beam, **M _{eff} increases while the K_{eff} remains the same.**

**So the natural frequency of the system is given by:**

\({\omega _n} = \sqrt {\frac{{{K_{eff}}}}{{{M_{eff}}}}} \)

and here, the numerator is constant while the denominator increases so overall,

**ω _{n} will decrease.**