In extreme conditions, even the most well-built of skyscrapers can sway 2.00 m with a frequency of up to 20.0 Hz due to high winds or seismic activity. A physical pendulum can be placed on the top of the skyscraper. As the skyscraper sways to the right, the pendulum swings to the left, reducing sway. Assuming the oscillations have a frequency of 0.500 Hz, design a pendulum that consists of a long beam of constant density, with a mass of 100 metric tons, a pivot point at one end of the beam, and a natural frequency of 0.500 Hz. What should be the length of the beam? Show all work
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
In extreme conditions, even the most well-built of skyscrapers can sway 2.00 m with a frequency of up to 20.0 Hz due to high winds or seismic activity. A physical pendulum can be placed on the top of the skyscraper. As the skyscraper sways to the right, the pendulum swings to the left, reducing sway. Assuming the oscillations have a frequency of 0.500 Hz, design a pendulum that consists of a long beam of constant density, with a mass of 100 metric tons, a pivot point at one end of the beam, and a natural frequency of 0.500 Hz. What should be the length of the beam? Show all work.
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