Explanation Given: Magnitude of periodic force is P m sin ω f t .Amplitude of vibration is 0.03 in at frequency 100 Hz . Maximum amplitude is x m = 4 × 10 − 5 in . Concept used: 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 block. Expression for the amplitude of forced vibration x m = ± δ s t ( 1 − ω f 2 ω n 2 ) ...... (2) Calculation: Substitute 4 × 10 − 5 in for x m , 0.03 in for δ s t and 2 π × 100 rad/s for ω f in equation (2) To determine (b) Range of force frequency.

12th Edition

ISBN: 9781260265521

Author: BEER

Publisher: MCG

See similar textbooks

Videos

Question

Chapter 19.4, Problem 19.105P

To determine

(a)

The spring stiffness for the vibration system.

To determine

(b)

Range of force frequency.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.4, Problem 19.104P

Chapter 19.4, Problem 19.106P

Students have asked these similar questions

"An automobile, weighing 1100lb empty and 3000 lb fully loaded, vibrates in a vertical direction while traveling at 55 mph on a rough road having a sinusoidal waveform with an amplitude Y ft and a period 12 ft. Assuming that the automobile can be modeled as a single-degree-of-freedom system with stiffness 30,000 lb/ft and damping ratio zeta=0.15, determine the amplitude ratio of vibration of the automobile when it is (a) empty . Answer with 2 decimal places" and (b) fully loaded

A 50-kg machine tool is mounted on an elastic foundation. An experiment is run todetermine the stiffness and damping properties of the foundation. When the tool is excitedwith a harmonic force of magnitude 8000 N at a variety of frequencies, the maximumsteady-state amplitude obtained is 2.5 mm, occurring at a frequency of 32 Hz. Use thisinformation to determine the stiffness and damping ratio of the foundation.

A mass of flexible machine part, m, of 10 ×1 kg was observed to vibrate badly at frequency of 10 Hz. The vibration was caused by the application of a harmonic force, F of 10 ×10N to the flexible part. A judgment was made by a mechanical engineer that the vibration was excessive because the frequency of the harmonic force coincides with the natural frequency of the flexible part. Analyze the mass and stiffness of an absorber that would eliminate vibrations of the flexible part at frequency of 10 Hz, if the amplitude motion of the absorber mass, Xa at 10 Hz was observed to be 0.1 × 3cm. (c) (d) If the flexible machine part is operated in the speed range of 500 to 750 rpm, justify whether the design of vibration absorber in Q3(c) is safe to be used or not.

Chapter 19 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

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.

(a) The spring stiffness for the vibration system.

Solution Summary: The author explains the spring stiffness for the vibration system.