## Under damping, Mechanical Engineering

Assignment Help:

Under Damping

If 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 = [(A1 + A2) cos ω t + i (A1 - A2) sin ω t]

= A0 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 . In absence of friction, = 0, the amplitude remains constant, i.e. equal to A0. In presence of friction, amplitude decays exponentially with time; the time t = τ = 1/ , 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.

#### Gear wheel mechanism, I want to tranfer the rotatory motion of my apache RT...

I want to tranfer the rotatory motion of my apache RTR 160 back wheel to a motor(of dynamo). kindly guide me with the design. i''m struck up in the gear wheel mechanism.

#### Front top view of the motorcycle part of motorcycle, Figure : Front Top Vie...

Figure : Front Top View of the Motorcycle Part No. Part Name Functions 1 Turn signal switch Used to give

#### Gears, how to prevent absolute noise during meshing of gears

how to prevent absolute noise during meshing of gears

#### Plasma welding, PLASMA WELDING This is an extension of TIG welding. In...

PLASMA WELDING This is an extension of TIG welding. In plasma welding torch, plasma energy is constricated and ensures its most efficient utilisation for welding cutting and s

#### Corrosion assessment of flare and vru system, Q. Corrosion Assessment of Fl...

Q. Corrosion Assessment of Flare and VRU System? The worst case scenario shall be considered during material selection of Flare KO Drums. Depending on the fluid composition ent

#### Steps for decarbonise the engine , The following steps are taken to decarbo...

The following steps are taken to decarbonise the engine : Remove the exhaust muffler. Disconnect the spark plug. Remove the intake pipe bolt. Loosen the bolt de

#### Ignition system-electrical system , Ignition System: The ignition system i...

Ignition System: The ignition system is a source and a means of initial spark required to start burning of fuel. A very high voltage supplied at the spark plug tip causes this spa

#### Tachometer-electrical instruments , Tachometer: This is used to measure th...

Tachometer: This is used to measure the speed (revolutions) of an engine in revolutions per minute (RPM). This is shown in Figure. Figure : Tachometer

#### Milling, milling machine time calcutation

milling machine time calcutation

#### #title.Thermal Engineering, what is zeroth law of thermodynamic ?

what is zeroth law of thermodynamic ?  