Explanation Given: Natural frequency is 2200 Hz . Equation of motion of box y = δ m sin ω f t . Acceleration of box δ m ω f 2 . Frequency of vibration f f . Concept used: Consider the system as shown below: Write the expression for amplitude of forced vibration. x m = δ m 1 − ( ω f 2 ω n 2 ) ...... (1) Here, x m is the amplitude of forced vibration, δ m is the maximum displacement, ω f is the forced frequency and ω n is the natural frequency of system. Write the Expression for total displacement. x = x m sin ω f t Substitute δ m 1 − ( ω f 2 ω n 2 ) for x m in the above expression. x = δ m sin ω f t 1 − ( ω f 2 ω n 2 ) ...... (2) Here, x is the total displacement. Write the expression for relative motion as. z = x − y Substitute δ m sin ω f t 1 − ( ω f 2 ω n 2 ) for x and δ m sin ω f t for y in above expression. z = ( δ m 1 − ( ω f 2 ω n 2 ) − δ m ) sin ω f t ...... (3) Here, z is the relative displacement. Write the general equation of relative displacement of motion. z = z m sin ω f t ...... (4) Here, z m is the maximum amplitude of relative displacement. Compare equation (4) and (3). z m = δ m ( ( ω f ω n ) 2 1 − ( ω f ω n ) 2 ) Multiply the above expression with ω n 2

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

See similar textbooks

Videos

Question

Chapter 19.4, Problem 19.123P

To determine

Percentage error with frequency of vibration of 600Hz.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.4, Problem 19.122P

Chapter 19.4, Problem 19.124P

Students have asked these similar questions

A single cylinder engine can be treated as a rotating unbalance model where the mass of the piston, m, acts at an eccentric distance, e which is half of the stroke. Determine the displacement amplitude of the engine in millimetres when it is rotating at a speed of 344.4 rpm. The engine parameters are: Mass of engine, M = 447.8 kg; keq = 220.3 kN/m; ceq = 2843.2 Ns/m; m = 10.6 kg and Stroke (i.e. 2e) = 236 mm. Give your answer to 2 dp. Answer:

T1= 0.62 s T2= 0.54 s K1= 2440 n/m

Question 2: A sensitive instrument of mass 100 kg is installed at a location that is subjected to harmonic motion with frequency 20 Hz and acceleration 0.5 m/s². If the instrument is supported on an isolator having a stiffness k = 25x10ª N/m and a damping ratio č = 0.05, determine the maximum acceleration experienced by the instrument. %3D

Chapter 19 Solutions

Vector Mechanics For Engineers

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - A 20-lb block is initially held so that the...Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - A 5-kg fragile glass vase is surrounded by packing...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.