The magnitude of the force per unit displaced is and thus, using the equation: Therefore: So the period of vertical oscillation is: 9. Describe an experiment using a simple pendulum to determine the value of acceleration due to gravity (g), deriving any formulae that will be required. The implies of experiments using a pendulum to determine the value of acceleration due to gravity, would be to tie a weight to the end of a piece of string, creating a pendulum. The time of the back and forth motion the pendulum shows is called the period. It does not depend on the mass or the size of the arc, only the length and acceleration due to gravity.
The formula for finding the period of a simple pendulum is: Where Period Length of pendulum Transpose the simple pendulum formula to find g: To solve the equations for any pendulum, time the pendulum through say 20 back and forth motions. Then record the time and divide it by 20 to find : Once has been found, measure the length of the pendulum, to the centre of the weight and input these values into the equations for . Now the acceleration due to gravity can be found. 10. Discuss forced mechanical vibration, resonance and damping in engineering, egg. Aircraft, bridges, ships, cars, etc.
Include the sequence of events and a description of the contribution of each to the final outcome. You are encouraged to draw on your own experience where you have been involved in a vibration issue on aircraft. Vibration can be described as the movement on a body, back and forth from its sting place when acted upon by an external force. There are three main parameters that can be measured from vibration. The first being amplitude, measuring how much vibration, frequency, measuring how many times it occurs in relation to time, and phase, which describes how it is vibrating.
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Forced mechanical vibration is when an external force from a mechanical imbalance causes oscillations through the system. For example when there is an imbalance on the rotors on a helicopter, the resulting vibrations travel through the aircraft. If the vibration matches the natural frequency of the aircraft, this can cause resonance. Resonance is a potentially destructive vibration as the oscillations will continue to grow in amplitude until the initial forced vibration ceases or failure occurs.
For example the well-known ground resonance test on a Chinook aircraft, where a vibration matches the natural frequency of the fuselage and rips itself apart. The likelihood of resonance can be minimized by the use of damping. Damping is the use of systems or components to reduce the amplitude of any oscillations to limit the damage vibrations can cause. This can be done in various ways; springs are used on ears suspension, viscous fluid is used in aircraft landing gear and on the Apache aircraft, rubber lead/lag dampers are used on the rotor head to minimizes the vibration from the blades.
An example where forced mechanical vibration leading to resonance has resulted in failure is the collapse of the Tacoma Narrows Bridge, Washington State, USA in 1940. Problems began to arise when on particularly windy days, construction workers on the bridge noticed that the deck oscillated vertically giving the bridge the nickname 'Galloping Grittier', nevertheless the bridge was opened to traffic on 1st July 1940. The 'Galloping motion continued and various attempts to correct it proved ineffective. These included extra strengthening cables and hydraulic dampers.
Fig 1 On the day of the collapse, 7th November 1940, the wind speed was MPH which resulted in, at first small oscillations of the deck. The wind caused a phenomenon known as rare elastic fluttering (fig 1), where the centre of the deck remains still and either side of the bridge twists in opposite directions. This then escalated into a resonance effect as the oscillations increased periodically. Once the vibration had Ovid past the bridges damping mechanisms and matched the natural frequency the result was unavoidable as resonance took hold (fig 2).
Fig 2 Further damping recommendations were made 5 days before the collapse of the bridge but were too late to save it. Two solutions were proposed: 1. To drill holes in the lateral girders and along the deck so that the airflow could circulate through them (reducing lift forces) 2. To give more aerodynamic shape to the transverse section of the deck by adding fairings or deflector vanes along the deck, attached to the girder fascia Lessons have been learnt from the collapse of the Tacoma Narrows
Bridge, the Bronx Whetstone Bridge, similar in design to the 'Galloping Grittier', was reinforced with fat high steel trusses on both sides of the deck shortly after the disaster to weigh down and stiffen the bridge to reduce oscillations. Thankfully no lives were lost in the collapse and as OTTOMH Amman (a leading bridge designer and a member of the investigation team) said when commenting on the new design of the bridge, ' if errors, or failure occur, we must accept them as a price for human progress'. My own experiences of vibration issues on aircraft are generally related to UT of balance rotors or drive shaft components.
There have been several instances of loose tail rotor shapeless due to vibration from the tail rotors and cracking on a cooling fan connected to the tail rotor drive due to a worn bearing hangar also causing vibration. Another example of a vibration issue I have been involved with, is struggling to track and balance the main rotors due to a modification which records stress on critical components. This modification altered the balance on the blades and rotor head due to extra weight from wires. Bibliography - Wisped
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