Using shock absorbers, you decide to damp the oscillations applying one shock ab

Question

Using shock absorbers, you decide to damp the oscillations applying one shock absorber to each spring. These shock absorbers apply a velocity-dependent drag force F = bv that opposes the motion of the bench. For proper damping, you decide that the motion of the bench should drop to half-amplitude within 0.479 seconds. (In other words, within 0.479 seconds the amplitude of motion should drop by a factor of one half.) When purchasing shock absorbers, what damping coefficient b should you specify to your industrial equipment supplier? (Assume that b2

Explanation / Answer

amplitude is ,

A=Ao*e^-bt

here

Ao.is maximum amplitude

b ...is damping co-efficent

but,

after t=0.479 sec A=1/2*Ao

now,

A=Ao*e^-bt

1/2*A0=A0*e^-b*0.479T

2=e^b*0.479

ln(2)=b*0.479

0.693=b*0.479

===> r=1.447 N*sec/m

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