Originally Posted by Astronuc
Are you asking about the original problem in this thread, or is this a new problem.
A force or load is applied to structure. There are live loads (e.g. traffic) and dead loads (the weight of the structure).
Pedestrians on a foot bridge do not normally walk with the natural frequency of a well designed bridge. Pedestrians do not normally walk in phase as a group.
I am asking about the original problem i.e. :
Consider an oscillating system of mass m and natural angular frequency omega_n. When the system is subjected to a periodic external (driving) force, whose maximum value is F_max and angular frequency is omega_d, the amplitude of the driven oscillations is
A= F_max / (sqrt((k-mw_d^2)^2+(bw_d)^2))
A= (F_max/m) / (sqrt((w_n^2-w_d^2)^2+(b(w_d)/m)^2))
where k is the force constant of the system and b is the damping constant.
(Assume that, when we walk, in addition to a fluctuating vertical force, we exert a periodic lateral force of amplitude 25 N at a frequency of about 1 Hz. Given that the mass of the bridge is about 2000 kg per linear meter, how many people were walking along the 144 m-long central span of the bridge at one time, when an oscillation amplitude of 75 mm was observed in that section of the bridge? Take the damping constant to be such that the amplitude of the undriven oscillations would decay to 1/e of its original value in a time t=6T, where T is the period of the undriven, undamped system.)