LAB 1
Effect of the great unwashed on Damping Characteristics Free Vibration
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Objective
To understand the effects of damping on the vibration and the effects of mass on the damping characteristics
Apparatus
* Aluminum Frame
* Vibrating Beam
* Spring
* Spring Attachments
* Damper
* Damper Attachments
* 3 C- clamps (qty 3)
* ADXL345 analog accelerometer development board
* Micro SD circular & card reader
* AAA batteries (qty 2)
* Weight Scale
Introduction
Logarithmic step-down, (?) is used to fancy the damping ratio of an under-damped system in the time domain. The logarithmic decrement is the natural log of the ratio of the amplitudes of the first two resultant peaks
Logarithmic decrement is given by
?=lnX1X2
If we consider the bone in amplitude in n successive cycles therefore the log decrement is given by
?=1nlnX0Xn
The damping ratio is a parameter, usually denoted by ? (zeta) that characterizes the frequency response of a second prescribe ordinary differential equation.
Damping ratio (?) can be compute by
?=?2?
Oscillation frequency (fn) can be compute by
fn=1T
Angular velocity ?n can be cipher by
?n=2?fn
Damping coefficient (c) can be calculated by
c=2??nm
This accelerometer records data in lowest material bit and it has a 10-bit root. The range for this device is ±4g.
This means that the resolution is:
210=1024 bits
±4g = 8g
1024 bits/8g = 128bits/g
Procedure
fragmentize 1: No Damper given over: (If your lab equipment has the damper already attached, please do Part 2 first, and come back to Part 1 afterwards)
1. appreciate the mass of the vibrating beam and record it
2. Measure the mass of the attachments on the beam and record it
3. Measure the mass of the clamps and record it
Items| Mass (kg)|
Mass of Aluminum Beam| 330 g|
1/3 Mass of Aluminum Beam| 110 g|
repel Assembly & U-clamp| 140 g|
1 - C clamp (3 Black ones)| 450 g...If you want to get a upright essay, order it on our website: Orderessay
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