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Vibration And Noise / Vibrasie en geraas - 354

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A pendulum with length L is connected to two springs with stiffness k.  The mass m of the pendulum can be seen as a point mass. Assume that the pendulum moves through small angles and that the springs only act horizontally on the pendulum. Assume the springs are not stretched or compressed at equilibrium. Assume that g equals 9.81 space straight m divided by straight s squared.

The equation of motion of the system can be written in the form:

A theta with ¨ on top space plus space B theta space equals space 0

Use these values to answer the following questions:

 m equals17 kgk equals773 straight N divided by straight m and L equalsstraight m.

NB: Provide your answer to two (2) decimal places and do not use any units in your final answer. Example: 2.099145... [m] should be entered as 2.10. Use SI-units in your answers.

Calculate the value of A.

'n Pendulum met lengte L is gebind aan twee vere met styfheid k.  Die massa mass m van die pendulum kan gesien word as 'n punt massa. Aanvaar dat die pendulum slegs met klein hoeke beweeg en dat die vere slegs horisontaal op die pendulum uitwerk. Aanvaar dat die vere nie by ewewig gerek of saamgedruk is nie. Aanvaar dat g equals 9.81 space straight m divided by straight s squared.

Die bewegingsvergelyking van die sisteem kan geskryf word in die vorm van:

A theta with ¨ on top space plus space B theta space equals space 0

Gebruik die waardes hieronder om die volgende vra te beantwoord:

 m equals17 kgk equals773 straight N divided by straight m en L equalsstraight m.

LW: Gebruik twee (2) desimale in die finale antwoord. Moet nie eenhede gebruik in die antwoord nie. Voorbeeld: 2.099145... [m] moet as 2.10 ingeskryf word. Gebruik SI-eenhede om vrae te beantwoord.

Bereken die waarde van A.

 

 

 

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Determine the natural frequency, omega subscript n, of the system in rad/s. 

Bepaal die natuurlike frekwensie, omega subscript n, van die sisteem in rad/s.

 

 

 

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If the two springs were to be replaced by a single spring at length L on the pendulum, what stiffness [unit: N/m] of the new spring will replicate the motion of the current system. 

As die twee vere deur 'n enkele veer  op lengte L op die pendulum vervang sou word, watter styfheid  [eenheid : N/m] van die nuwe veer sal die beweging van die huidige stelsel herhaal.

 

 

 

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What effect will a larger pendulum mass have on the natural frequency of the system?

Wat sal die uitwerking op die natuurlike frekwensie van die stelsel wees as die pendulum swaarder gemaak word?

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Calculate the value of B.

Bereken die waarde van B.

 

 

 

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What effect will a longer pendulum have on the natural frequency of the system?

Wat sal die uitwerking op die natuurlike frekwensie van die stelsel wees as die pendulum langer gemaak word?

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