Under damping, Mechanical Engineering

Assignment Help:

Under Damping

If  2251_download.png  the restoring force is larger than friction, and the oscillation is classified as under-damped. In this case, ω is real and behaves exactly like the solution of an undamped oscillator. Hence, we have


q =  469_download (1).png [(A1 + A2) cos ω t + i (A1 - A2) sin ω t]

= A0  469_download (1).png  sin (ω t + Ø) = A ( t ) sin (ω t + Ø)

where we used, A1 + A2 = A sin Ø    and     i (A1 - A2) = A cos Ø

The above solution shows that particle performs oscillations with frequency ω, or time period T = 2 π/ω, but with a time dependent A ( t ) = A0  469_download (1).png . In absence of friction,  1255_download (2).png  = 0, the amplitude remains constant, i.e. equal to A0. In presence of friction, amplitude decays exponentially with time; the time t = τ = 1/ 1255_download (2).png , when amplitude becomes 1/e of its initial value is called decay constant of the oscillator. That is,

A( t ) = A0 e-t/τ

= A0/e    at t = τ


where A0 is the initial amplitude (or displacement) at t = 0.


Related Discussions:- Under damping

Surging, what is surging in turbo machines subject

what is surging in turbo machines subject

Process to establish standard time for completion of a job, a) What is meth...

a) What is method study. Define various stages of method study. b) What are main techniques used to study path of movement in method study. a) Discuss the process to establis

Motion of this particle, Motion of this particle: A particle of mass m...

Motion of this particle: A particle of mass m is resting on a smooth horizontal plane as illustrated in Figure (a). It is associated to a spring which has a constant of k in f

Basic formula for maximum bending moment, Q.  W rite down the basic form...

Q.  W rite down the basic formula for maximum bending moment in some ideal cases. Sol.:   Ber m together with nature of load Maximu

Stress concentration factor, 1. Write a short note (not more than half A4 p...

1. Write a short note (not more than half A4 page) on your understanding on St. Venant's Principal for your engineering design analysis. 2.  Estimate the " Stress Concentration

Explain fundamental of metal casting, Q. Explain Fundamental of metal casti...

Q. Explain Fundamental of metal casting? (1)Melting the material (2)Allowing the molten metal to cool and solidify in the mould "A plane where the castings are made is ca

Find out the centroid of the shaded area, Find out the centroid of the shad...

Find out the centroid of the shaded : Find out the centroid of the shaded area shown in Figure Solution Net area of shaded portion of Figure = The area of full

Evaluate the speed of wheel, In an epicyclic gear train, the internal wheel...

In an epicyclic gear train, the internal wheels B and A and compound wheels C and D rotate independently about axis O. The wheels E and F rotate on pins fixed to the arm G. E gear

Kinematic and dynamics, In Figure P4.2 , ?1 = 200 rad/s cw and a1 = 4000 ra...

In Figure P4.2 , ?1 = 200 rad/s cw and a1 = 4000 rad/s2 cw, Find the acceleration of points B, C, and D and the angular acceleration of link 2?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd