A body of mass \(m\) is suspended by a spring of constant \(k\) and attached to an elastic beam of length \(l\), as shown in Figure 2.49. When the mass is attached to the spring, measurements are taken of the spring extension \(\delta_{s}\) and the end deflection of the beam \(x_{b}\). Neglect the masses of the beam and the spring.

(a) Estimate the natural frequency of the system.

(b) Calculate the natural frequency if the mass is attached to the beam directly without a spring.

(c) Calculate the natural frequency if the beam is assumed to be rigid.

(d) Calculate the respective numerical values given \(\delta_{s}=12 \mathrm{~mm}, x_{b}=2 \mathrm{~mm}\), and \(l=0.5 \mathrm{~m}\).

Transcribed Image Text:

0000000 k m T X m Figure 2.49: Mass suspended by a spring from a beam.