# SolSec 2.3 - 2 24 Problems and Solutions Section 2.3(2.32...

This preview shows pages 1–4. Sign up to view the full content.

2- 24 Problems and Solutions Section 2.3 (2.32 through 2.36) 2.32 Referring to Figure 2.10, draw the solution for the magnitude X for the case m = 100 kg, c = 4000 N s/m, and k = 10,000 N/m. Assume that the system is driven at resonance by a 10-N force. Solution: Given: m = 100 kg, c = 4000 N s/m, k = 10000 N/m, o F = 10 N, ! = n = k m = 10 rad/s = tan ! 1 cw k ! m " 2 # \$ % & ( = tan ! 1 (40,000) (10,000 ! 10,000) # \$ % & ( = 90 ° = ) 2 rad From the figure: X = F o k ! m 2 ) 2 + ( c ) 2 = 10 (10,000 ! 10,000) 2 + (40,000) 2 X = 0.00025 m c ω X F 0 ( k - m ω 2 ) X φ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2- 25 2.33 Use the graphical method to compute the phase shift for the system of Problem 2.32 if ω = ω n /2 and again for the case ω = 2 ω n . Solution: From Problem 2.32 ! n = 10 rad/s (a) = n 2 = 5 rad/s X = 10 (10,000 ! 2500) 2 + (20,000) 2 = .000468 m kX = (10,000)(.000468) = 4.68 N c ω X = (4000)(5)(.000468) = 9.36 N m 2 X = (100) 2 ) 5 ( (.000468) = 1.17 N From the figure given in problem 2.32: = tan ! 1 9.36 4.68 ! 1.17 " # \$ % = 69.4 ° = 1.21 rad (b) = 2 n = 20 rad/s X = 10 (10000 ! 40000) 2 + (80000) 2 = .000117 m kX = (10000)(.000117) = 1.17 N c X = (4000)(20)(.000117) = 9.36 N m 2 X = (100) 2 ) 20 ( (.000117) = 4.68 N From the figure: = tan ! 1 9.36 1.17 ! 4.68 " # \$ % & = ! 69.4 ° = ! 1.21 rad
2- 26 2.34 A body of mass 100 kg is suspended by a spring of stiffness of 30 kN/m and dashpot of damping constant 1000 N s/m. Vibration is excited by a harmonic force of amplitude 80 N and a frequency of 3 Hz. Calculate the amplitude of the displacement for the vibration

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

SolSec 2.3 - 2 24 Problems and Solutions Section 2.3(2.32...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online