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 : Undamped free vibration

Objective : Determining the natural frequency of a Undamped free vibration of a mass spring system.

Theory :

Newton’s 2nd law

∑ F=m y …………………….………. ( Equation 1 )

Hence, −ky=m y ………………….……... ( Equation 2 )

Rearrange Equation 2

y+ω

n2y=0

.………..………………... ( Equation 3 )

where natural frequency of the system,

ωn=√ km …..…….………..........……... ( Equation 4 )

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

Free body diagram :

MD. Atiqur Rahman Faisal


Procedure :

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

0 2 4 6 8 10 120

2

4

6

8

10

12

01-Weight vs Extension of the spring

01-Weight vs Extension of the spring

265−56

=43.33(avg ƭ )



0 2 4 6 8 10 120

2

4

6

8

10

12

02-Weight vs Extension of a spring

02-Weight vs Extension of a spring

358−226

=56 (avg ƭ )

0 2 4 6 8 10 120

2

4

6

8

10

12

03-Weight vs Extension of a spring system

03-Weight vs Extension of a spring system

362−66

=59.33(avg ƭ )



0 2 4 6 8 10 120

2

4

6

8

10

12

04-Weight vs Extension of loaded spring system

04-Weight vs Extension of loaded spring system

410−206

=65(avg ƭ )

0 2 4 6 8 10 120

2

4

6

8

10

12

05-Weight vs Extension

05-Weight vs Extension

454−316

=70.5(avg ƭ )

Vibrating motion oscillating :



0 2 4 6 8 10 120

2

4

6

8

10

12

01-Vibrating motion oscillating

01-Vibrating motion oscil-lating

0 2 4 6 8 10 120

2

4

6

8

10

12



0 2 4 6 8 10 120

2

4

6

8

10

12





0 2 4 6 8 10 120

2

4

6

8

10

12



0 2 4 6 8 10 120

2

4

6

8

10

12



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.


Undamped Free Vibration

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