Chapter 16: Problem 9: Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.6 × 10⁵ kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building. a) What effective force constant, in N/m, should the springs have to make them oscillate with a period of 2.4 s? b) What energy, in joules, is stored in the springs for a 1.2 m displacement from equilibrium?
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.
Chapter 16: Problem 9: Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.6 × 10⁵ kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building.
a) What effective force constant, in N/m, should the springs have to make them oscillate with a period of 2.4 s?
b) What energy, in joules, is stored in the springs for a 1.2 m displacement from equilibrium?
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