Following is the response of a forced undamped vibration sys

Following is the response of a forced undamped vibration system. Calculate beat frequency natural frequency and forcing frequency.

Solution

a) Beat frequency is the frequency of the outer envelop of the amplitudes of all ycles of the response of the forced undamped vibration.

Frequency is the number of cycles per unit time. It is also equal to 1/Time period.

From the given graph, we can see that the time for one half cycle of Beat is approximately 1.35 sec. The full cycle time or time period is 2.7 sec.

Hence Beat frequency = 1/Time period=1/2.7 cycles/sec=0.37 cycles/sec.

b) Similarly, the naural frequncy = No of cyles of actual wave/unit time

From the graph it is found that there are about 3 full cycles in aproximately 0.4 sec.   

Natural frequency = 3/0.4=7.5 cycles/sec.

c) For beats, Beat frequency= (Natural frequency-Forcing frequency)/2.

Forcing frequency= Natural Frequency-2xBeat frequency

=7.5-2x0.37

=6.76 cycles/sec.