Explanation Given information: The weight of the block ( W ) is 64 lb . The spring constant ( k ) is 1 kip/ft . The magnitude of the force ( P ) is P m sin ω f t . The forced circular frequency ( ω f ) is 10 rad/s . The amplitude of motion ( x m ) is 0.75 in . or 0.0625 ft . The acceleration due to gravity ( g ) is 32.2 ft/s 2 . Calculation: Calculate the mass of the block ( m ) using the formula: W = m g m = W g Substitute 64 lb for W and 32.2 ft/s 2 for g . m = 64 32.2 = 1.9876 lb ⋅ s 2 / ft Calculate the natural circular frequency ( ω n ) using the formula: ω n = k m Substitute 1 kip/ft for k and 1.9876 lb ⋅ s 2 / ft for m . ω n = 1 × 1000 lb/ft 1.9876 lb ⋅ s 2 / ft = 22

12th Edition

ISBN: 9781260804638

Author: BEER

Publisher: MCG

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 19.102P

To determine

Find the constant force (Pm).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.4, Problem 19.101P

Chapter 19.4, Problem 19.103P

Students have asked these similar questions

A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dash-pot at unit velocity ; 2. the ratio of the frequency of the damped vibration to the frequency of the undamped vibration ; and 3. the periodic time of the damped vibration.

A slender 10-kg bar AB with a length of l = 0.6 m is connected to two collars of negligible weight. Collar A is attached to a spring with a constant of k = 1.5 kN/m and can slide on a horizontal rod, while collar B can slide freely on a vertical rod. Knowing that the system is in equilibrium when bar AB is vertical and that collar A is given a small displacement and released, determine the period of the resulting vibrations.

A 6-kg uniform cylinder is assumed to roll without sliding on a horizontal surface and is attached by a pin at point C to the 4-kg horizontal bar AB. The bar is attached to two springs, each having a constant of k = 3.5 kN/m, as shown. Knowing that the coefficient of static friction between the cylinder and the surface is 0.5, determine the maximum amplitude of the motion of point C that is compatible with the assumption of rolling.

Chapter 19 Solutions

VECTOR MECHANICS FOR ENGINEERS W/CON >B

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 - Prob. 19.6P 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 - Prob. 19.10P

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.

Find the constant force ( P m ) .

Solution Summary: The author calculates the mass of the block (m) using the formula: cW=mg m=

Concept explainers

Videos

Find the constant force (Pm).

Want to see the full answer?

Chapter 19 Solutions