Explanation Given information: The coefficient of damping is c . The amplitude of the motion is x m . The circular frequency of the harmonic force is ω f . Calculation: The expression for the steady state response ( x ) of the machine as follows: x = x m sin ( ω f t − ϕ ) Differentiate the above equation with respect to time ‘ t ’. d x d t = x m ω f cos ( ω f t − ϕ ) d x = x m ω f cos ( ω f t − ϕ ) d t Calculate the force transmitted ( F d ) to the machine for the dashpot using the relation: F d = c d x Substitute x m ω f cos ( ω f t − ϕ ) for dx . F d = c x m ω f cos ( ω f t − ϕ ) Calculate the work done in a complete cycle ( E ) using the relation: E = ∫ F d d x Here, F d is the force and dx is the distance. Substitute c x m ω f cos ( ω f t − ϕ ) for F d and x m ω f cos ( ω f t − ϕ ) d t for dx . E = ∫ c x m ω f cos ( ω f t − ϕ ) x m ω f cos ( ω f t − ϕ ) d t = ∫ c x m 2 ω f 2 cos 2 ( ω f t − ϕ ) d t Differentiate the above equation with respect to time ‘ t ’ in the limit from 0 to 2 π ω f . E = ∫ 0 2 π ω f c x m 2 ω f 2 cos 2 ( ω f t − ϕ ) d t [ cos 2 ( ω f t − ϕ ) = 1 − 2 cos ( ω f t − ϕ ) 2

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

Question

Chapter 19.5, Problem 19.150P

To determine

Show that the mechanical energy dissipated per cycle by the dashpot is E=πcxm2ωf.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.5, Problem 19.149P

Chapter 19.5, Problem 19.151P

Students have asked these similar questions

Refrigerant-134a is expanded isentropically from 600 kPa and 70°C at the inlet of a steady-flow turbine to 100 kPa at the outlet. The outlet area is 1 m2, and the inlet area is 0.5 m2. Calculate the inlet and outlet velocities when the mass flow rate is 0.65 kg/s. Use the tables for R-134a. The inlet velocity is m/s. The outlet velocity is m/s.

A container filled with 70 kg of liquid water at 95°C is placed in a 90-m3 room that is initially at 12°C. Thermal equilibrium is established after a while as a result of heat transfer between the water and the air in the room. Assume the room is at the sea level, well sealed, and heavily insulated. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the final equilibrium temperature. Use the table containing the ideal gas specific heats of various common gases. The final equilibrium temperature is °C.

Steam at 100 psia and 650°F is expanded adiabatically in a closed system to 10 psia. Determine the work produced, in Btu/lbm, and the final temperature of steam for an isentropic expansion efficiency of 80 percent. Use steam tables. The work produced is Btu/lbm. The final temperature of steam is °F.

Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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.

Show that the mechanical energy dissipated per cycle by the dashpot is E = π c x m 2 ω f .

Solution Summary: The author explains that the mechanical energy dissipated per cycle by the dashpot is E=pi cxm2omega _f.

Concept explainers

Show that the mechanical energy dissipated per cycle by the dashpot is E=πcxm2ωf.

Want to see the full answer?

Chapter 19 Solutions