Consider a rod with concentrated mass m attached at its end shown in Fig B2 Obta
ID: 1409554 • Letter: C
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