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1. The problem statement, all variables, and given/known data
Describe the energy conversions in a spring undergoing simple harmonic motion as it moves from the point of maximum compression to maximum stretch in a frictionless environment. Focus on points at which there will be maximum speed, minimum speed, minimum acceleration.
b) Explain what is meant by damping, give an example of a technology that requires a damping mechanism and describe how it takes place.
The attempt at a solution
i) Maximum speed.
The maximum speed of an oscillating spring would be when it is at the equilibrium. At this point all the gravitational energy would be converted to kinetic energy.ii) Minimum speed.
The speed of an oscillating spring would be minimum at two places, the max compression and when the spring has reached it max stretch. At these points there would be no kinetic energy.iii) Minimum acceleration.
Acceleration is at its minimum when at equilibrium.a) Dampening is a decrease in the amplitude of oscillation until it decreases to 0. This is usually due to forces such as air resistance and friction. An example of dampening is in the tower Taipei 101. This tower is known as the Taipei World Financial Center. This is where the largest tuned mass damper is located. This stabilizes the building and protects it from violent motion. This violent motion is usually due to environmental forces such as earthquakes. Another example we could use is a piano, or more specifically the grand piano. Basically, when you press and hold on a key it causes a hammer to transfer all that energy to a string which vibrates and causes the damper to be lifted and this causes the string to continue oscillating until it slowly comes to a stop. If you simply press and let, go of the key right away the damper will take the energy away from the note giving it less time to oscillate. There’s even a “damper” pedal on a piano that would actually lift the dampers and allow the note to be drawn out longer.
Thank you!
Describe the energy conversions in a spring undergoing simple harmonic motion as it moves from the point of maximum compression to maximum stretch in a frictionless environment. Focus on points at which there will be maximum speed, minimum speed, minimum acceleration.
b) Explain what is meant by damping, give an example of a technology that requires a damping mechanism and describe how it takes place.
The attempt at a solution
i) Maximum speed.
The maximum speed of an oscillating spring would be when it is at the equilibrium. At this point all the gravitational energy would be converted to kinetic energy.ii) Minimum speed.
The speed of an oscillating spring would be minimum at two places, the max compression and when the spring has reached it max stretch. At these points there would be no kinetic energy.iii) Minimum acceleration.
Acceleration is at its minimum when at equilibrium.a) Dampening is a decrease in the amplitude of oscillation until it decreases to 0. This is usually due to forces such as air resistance and friction. An example of dampening is in the tower Taipei 101. This tower is known as the Taipei World Financial Center. This is where the largest tuned mass damper is located. This stabilizes the building and protects it from violent motion. This violent motion is usually due to environmental forces such as earthquakes. Another example we could use is a piano, or more specifically the grand piano. Basically, when you press and hold on a key it causes a hammer to transfer all that energy to a string which vibrates and causes the damper to be lifted and this causes the string to continue oscillating until it slowly comes to a stop. If you simply press and let, go of the key right away the damper will take the energy away from the note giving it less time to oscillate. There’s even a “damper” pedal on a piano that would actually lift the dampers and allow the note to be drawn out longer.
Thank you!
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