Question

An unhappy 0.300kg rat, moving on the end of spring with a spring constant,             

     k = 2.50N/m, is acted upon by a damping force, F_x = -bv_x.

1. If the constant, b, has a value of 0.900kg/s, what is the frequency of oscillation of the rat?

2. For what value of the constant , b, will the motion be “critically” damped?

Answer 1

Given values are

Spring constant is k = 2.50N/m

Mass of rat is m= 0.300kg

Damping constant is b= 0.900kg/s

a)

Using formula of angular frequency for damped Oscillation

w' = ( (k/m) - ( (b^2)/(4m^2) ) )^(1/2)

therefore putting values in above equation we get W'=2.47 radian/s

then converting this into hertz

f' = w'/2

f' = 0.393 Hz

b)

the condition for critical damping is

b= 2 x ( (km)^(1/2) )

on putting values in above equation & Solving we get

b=1.73 kg/s