Explanation Given: The spring constant is k . Magnitude of periodic force is P m sin ω f t . Amplitude of vibration should be three times of static deflection. Concept used: Write the expression for the natural frequency of the system. ω n = k m ...... (1) Here, ω n is the natural frequency of system, k is the spring constant and m is the mass of collar. Write the expression for static deflection in the system caused by the constant force of magnitude P m as. δ s t = P m k ...... (2) Here, δ s t is the static deflection and P m is the constant force. Write the expression for the amplitude of forced vibration. x m = δ s t ( 1 − ω f 2 ω n 2 ) ...... (3) Calculation: Case 1: Consider the amplitude of forced vibration exceeds positively three times the static deflection. x m > 3 δ s t Substitute δ s t ( 1 − ω f 2 ω n 2 ) for x m in the above expression. δ s t ( 1 − ω f 2 ω n 2 ) > 3 δ s t 1 ( 1 − ω f 2 ω n 2 ) > 3 ( 1 − ω f 2 ω n 2 ) < 1 3 ω f ω n > 2 3 Simplify the above expression for ω f . ω f > ω n 2 3 ...... (4) Case 2: Consider the amplitude of forced vibration exceeds negatively three times the static deflection. x m < − 3 δ s t Substitute δ s t ( 1 − ω f 2 ω n 2 ) for x m in the above expression

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

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Videos

Question

Chapter 19.4, Problem 19.101P

To determine

The range of values of ωf for which the amplitude of the vibrations exceeds three times the static deflection.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.4, Problem 19.100P

Chapter 19.4, Problem 19.102P

Students have asked these similar questions

Using graphical methods, draw the pressure angle at the position shown in (a) and (b). e |------- R = Cam Base Radius e = Follower Offset ẞ₁ = Section Duration 1 B₁ = Section Duration 2 ẞ₂ = Section Duration 3 В2 B₁ Follower Position ww R ẞ3 (a) Reference Radial (b)

The figure below illustrates a graph that has a variable load torque and constant drive torque. Each cycle lasts three revolutions (6л radians). Torque (N-m) 600 550 400 1 200 TD= 225 N-m 2 + -T₁ 3 4 1 + 0 In addition, the rotation speed is @o steady-state conditions, determine 1. the average power required, 2πT 4π 5πT 6п Ꮎ = 180° rpm = 18.85 rad/sec, Imachine 125 kg-m². Assuming 2. the maximum and minimum rotational speeds throughout a cycle, 3. the mass of a 0.6-meter-diameter solid disc flywheel to produce Cs = 0.025.

An elastic cord is stretched between 2 points A and B located 2y = 0.8 m apart in the horizontal plane. When stretched directly between A and B, the tension is P₂ = 40 N. The cord is then stretched as shown until its midpoint C has moved through x = 0.3 m to C', and a force of F = 240 N is required to hold the cord at C'. A pellet (m = 0.1 kg) is placed at C' and the cord is released. Find the speed of the pellet as it passes through C.

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.

The range of values of ω f for which the amplitude of the vibrations exceeds three times the static deflection.

Solution Summary: The author analyzes the range of values of omega, where the amplitude of the vibration exceeds positively three times the static deflection.

Concept explainers

Videos

The range of values of ωf for which the amplitude of the vibrations exceeds three times the static deflection.

Want to see the full answer?

Chapter 19 Solutions