Undamped Free Vibration

STUDENT NAME

MD ATIQUR RAHMAN FAISAL

STUDENT ID

SCM-012154

COURSE

BACHELOR IN MECHANICAL ENGINEERING

LECTURER

DR. CHIA

SUBMISSION DATE

24th April 2012

SUBJECT

ENGINEERING MECHANICS (EAT 203)

Undamped free vibration

Title

:

Objective : spring system. Theory

Undamped free vibration Determining the natural frequency of a Undamped free vibration of a mass

: Newton’s 2nd law



 F  my …………………….………. ( Equation 1 )

Hence,  ky  my ………………….……... ( Equation 2 ) Rearrange Equation 2  y  n y  0 .………..………………... ( Equation 3 ) 2

where natural frequency of the system,

n 

k …..…….………..........……... ( Equation 4 ) m

Apparatus : Displacement measuring plate and displacement measuring transducer, spring weight and loading rod. Free body diagram

:

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Undamped free vibration

Procedure

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1. Determining the stiffness of the spring, a) The length of the unloaded spring is measured. b) A weight is loaded on the loading rod with the plate, and then the loading rod is anchor to the spring. c) The extension of the loading rod is captured. d) Steps 2 and 3 are repeated with different loading condition. 2. Determining the natural frequency of the mass spring system, a) A weight is loaded on the loading rod with plate, and anchored with the spring. b) The displacement transducer is placed in such a way that the probe is at right angle to the plate at the loading rod. c) The “quickDAQ” is run on the PC to set the sample rate channel to 1000,(i.e. 1000 data captured per second) and recording time 10 seconds. d) The play button is clicked to capture the initial displacement of the system. (it is noted the displacement measure transducer express it’s reading in voltage) e) The graphical user interface data are saved using the name “initial displacement.csv”. f) The loading rod is displaced slightly, and the motion of the vibrating system is captured using play button. g) The data are saved on the name “final displacement.csv”. h) Steps “a to g”, are repeated with four different loading condition. The data file name was saved in serials, so that no of the file are overwritten.

Graph

01-Weight vs Extension of the spring 7 6 5 4 3 2 1 0 -1 0 -2 -3 -4

01-Weight vs Extension of the spring 100

MD. Atiqur Rahman Faisal

200

300

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Undamped free vibration

02-Weight vs Extension of a spring 8 6 4 2 0 -2

0

100

200

300

400

500

02-Weight vs Extension of a spring

-4 -6 -8

03-Weight vs Extension of a spring system 6 4 2 0 0

100

200

300

400

500

03-Weight vs Extension of a spring system

-2 -4 -6

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Undamped free vibration

04-Weight vs Extension of loaded spring system 3 2 1 0 -1 0 -2 -3 -4 -5 -6 -7

200

400

600

04-Weight vs Extension of loaded spring system

05-Weight vs Extension 3 2 1 0 -1 0

100

200

-2

300

400

500

600 05-Weight vs Extension

-3 -4 -5 -6 -7

Vibrating motion oscillating :

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Undamped free vibration

01-Vibrating motion oscillating 9 8 7 6 5 4 3 2 1 0 -1 0 -2

01-Vibrating motion oscillating

100

200

300

02-Vibrating motion oscillating 14 12 10 8 02-Vibrating motion oscillating

6 4 2 0 0

100

200

300

400

500

03-Vibrating motion oscillating 10 8 6 03-Vibrating motion oscillating

4 2 0 0

100

200

300

400

500

-2

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Undamped free vibration

04-Vibrating motion oscillating 9 8 7 6 5

04-Vibrating motion oscillating

4 3 2 1 0 0

200

400

600

05-Vibrating motion oscillating 9 8 7 6 5 05-Vibrating motion oscillating

4 3 2 1 0 -1 0

200

400

600

Discussion and conclusion When the spring is allowed to swing independently, it can swing longer time than carrying a load on it. When a mass is loaded on a spring, and allowed to swing, its amplitude decreases with time but the frequency remains constant, and slowly comes to rest. According to Newton’s third law of motion, every action has an equal and opposite reaction. When the spring with mass is allowed to swing freely, viscous drag force acting on the spring, to its opposite direction, air resistance also acts on the object to slow down its amplitude. That is the reason the motion become damped. In real life there is no Undamped situation, because some external resistance will be always present.

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