SolSec1.7 - Problems and Solutions Section 1.7 (1.73...

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Problems and Solutions Section 1.7 (1.73 through 1.79) 1.73 Choose a dashpot's viscous damping value such that when placed in parallel with the spring of Example 1.7.2 reduces the frequency of oscillation to 9 rad/s. Solution: The frequency of oscillation is ωω ζ d n =− 1 2 From example 1.7.2: ω n mk == = 10 10 10 3 rad/s, kg, and N/m So, 91 01 2 ⇒= = 09 1 1 22 2 .( . ) ζζ () 436 . 0 9 . 1 2 = = Then cm n = 2 2 10 10 0 436 87 2 ωζ ( )( )( . ) . kg/s 1.74 For an underdamped system, x 0 = 0 and v 0 = 10 mm/s. Determine m, c, and k such that the amplitude is less than 1 mm. Solution: Note there are multiple correct solutions. The expression for the amplitude is: Ax vx xA vv on o d o o d d o 2 0 2 2 2 0 0 001 0 001 001 0 001 10 =+ + =⇒ = < ⇒ > = = . . . . ζω for m So d k m k m km > ⇒− >⇒ = 11 0 1 100 100 1 2 2 2 , (1) Choose =⇒ > 0 01 100 01 .. k m (2) Choose > 1 100 01 kg . (3) Choose k = 144 N/m > 100.01 = = n d n 144 12 11 99 20 2 4 rad s rad s rad s kg s . .
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1.75 Repeat problem 1.74 if the mass is restricted to lie between 10 kg < m < 15 kg. Solution: Referring to the above problem, the relationship between m and k is k >1.01x10 -4 m after converting to meters from mm.
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SolSec1.7 - Problems and Solutions Section 1.7 (1.73...

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