Essay about undamped cost-free vibration

undamped free oscillation


To determine the natural frequency intended for an undamped spring mass system. INTRODUCTION

Vibration is definitely the periodic action of a physique or system of connected body displaced coming from a position of equilibrium. It is a mechanical trend whereby amplitude occur about an balance point. The oscillations can be periodic or perhaps random. Cost-free vibration arises when a mechanical system is trigger with an initial input and after that allowed to vibrate freely. If there is no external force applied to the system, the machine will knowledge free vibration. Motion in the system will probably be established by a basic disturbance. Furthermore, if there is zero resistance or perhaps damping inside the system, the oscillatory motion will continue forever with constant extravagance. Such a system is called undamped. Through this experiment the natural rate of recurrence for a great undamped springtime mass system is to be decide by using a mass-spring-damper. THEORY

Newton's 2nd legislation

 ……………………. ………. ( Formula 1 )

Hence, …………………. ……... ( Equation a couple of )

Rearrange Equation 2

. ……….. ………………... ( Formula 3 )

where normal frequency in the system,

….. ……. ……….......... ……... ( Formula 4 )


Displacement measuring transducer and displacement testing plate, springtime, weights, loading rod. PROCESS

Determine the stiffness from the spring

The size of the unloaded spring was measured.

A weight was inserted unto the loading rod (with plate), then the loading fly fishing rod was anchored to the spring.

The extension of the loaded early spring was known.

Steps 2 to 3 were repeated with four various other different packing conditions. Identify the natural frequency in the spring-mass system

A fat was placed unto the loading fly fishing rod (with plate), then the launching rod was anchored towards the spring.

The displacement transducer was arranged in such a fashion that the probe is at right angle to the plate within the loading rod.

The ‘quickDAQ' was operate on the COMPUTER then the ‘Sample Rate per Channel' was set multitude of and the ‘Recording time' was set to twelve seconds.

The ‘Play' button was clicked on to capture your initial displacement with the system.

The data was saved under ‘initial shift. csv' utilizing the Save Because function in the graphic graphical user interface.

The packing rod was slightly displaced and the movement of the moving system was captured by using the ‘Play' key.

The data was saved underneath ‘final shift. csv'.

Measures 1 to 7 had been repeated with four additional different launching conditions.


Mass (kg)Weight (N)Extension(cm)

0013. 7

zero. 43. 92415. 0

zero. 65. 88617. 0

0. 87. 84818. 0

1 . 09. 81020. 0

Big t = (326-92 /100) sama dengan 2 . 34s

П„ =(Time, T)/(number of cycle)


П„ = 2 . 34/6

= 0. 39 s



= 2ПЂ/0. 39

sama dengan 16. 14 rads^(-1)

Assumptive Value (0. 4kg):

Lean of the chart, K= 196. 64 N/m

П‰_(n sama dengan в€љ(k/m))

meters = dumbbells mass (kg) + Fly fishing rod mass (kg) + dish mass (kg) + diamond ring (kg) + ring (kg) m = 0. 40kg + zero. 33kg +0. 03kg+0. 03kg

m sama dengan 0. 79kg

П‰n= в€љ(( 196. 64)/0. 79)

sama dengan 15. 79 гЂ–radsгЂ—^(-1)

Percentage Error = ((Theoretical value – Fresh value))/(( Theoretical value)) × 100%

sama dengan (|15. 78-16. 11|)/((15. 78))Г—100%

= installment payments on your 09%

Capital t = (518-228 /100) = 2 . 90s

П„ =(Time, T)/(number of cycle)


П„ = installment payments on your 90/6

= 0. twenty four s



= 2ПЂ/0. 39

sama dengan 13. 09 rads^(-1)

Theoretical Value (0. 4kg):

Lean of the graph, K= 196. 64 N/m

П‰_(n = в€љ(k/m))

meters = weight loads mass (kg) + Fishing rod mass (kg) + platter mass (kg) + ring (kg) + ring (kg) m = 0. 60kg + 0. 33kg +0. 03kg+0. 03kg

m sama dengan 0. 99kg

П‰n= в€љ(196. 64/0. 99)

= 16. 09 гЂ–radsгЂ—^(-1)

Percentage Problem = ((Theoretical value – Experimental value))/(( Theoretical value)) × fully

= (|14. 09-13. 09|)/((14. 09))Г—100%

sama dengan 7. 10%

T sama dengan (420-104 /100) = three or more. 16s

П„ =(Time, T)/(number of cycle)...