Consider a rod with concentrated mass m attached at its end shown in Fig B2 Obta

Question

Consider a rod with concentrated mass m attached at its end shown in Fig B2 Obtain an expressions for the natural frequencies of longitudinal rod. treating the rod as a distributed-parameter (continuous) Find the fundamental (lowest) oscillation frequency assuming that the rod mass is 0.01m (that is much smaller than the concentrated Calculate spatial and temporal fundamental frequencies for length L=0.5 m. Density of steel 7.8 g/cm^5 and the The wave equation for longitudinal motion of where c is the wave propagation The deflection of the rod. u(x.t). satisfies Ho degree tensile stress.

Explanation / Answer

a) Expression of natural frequencies :-

=>    f = n * [sqrt(T/k)]/2L

where, k = mass per unit length of string

            T = tension in string

            L = Length of string

b)    Here, fundamental frequency =   n * [sqrt(T/k)]/2L

                                                          =   1 * [sqrt(0.098/10-3)]/(2*0.5)

                                                          = 9.9 Hz

    => spatial fundamental frequency = 19.8 Hz

=> temporal fundamental frequency = 4.96 Hz

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