Question

For the given parameters for a forced mass-spring-dashpot system with equation mx"+ cx' + kx = Fo cos ot. Investigate the possibility of practical resonance of this system. In particular, find the amplitude C(a) and find the practical resonance frequency o (if any). m 1, c 5, k 40, Fo = 50

Answer 1

Practical resonance occurs if:

k C > 0 2m2 m

for our case, with the values given,

k C 27.5 0 2m2 m

Therefore, practical resonance is possible.

Practical resonance frequency is given by:

2 k w = 2m2 m

........... practical resonance frequency

w= 27.5 = 5.2440Hz

amplitude:

Fo VIk - mu2)2(cw)2

............amplitude

= 1.7213m C (w)

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