On December 29, 1997, a United Airlines flight from Tokyo to Honolulu was hit with severe turbulence 31 minutes aftertakeoff. Data from the airplane’s “black box” indicated that the 747 moved up and down with an amplitude of 30.0 mand a maximum acceleration of 1.8g. Treating the up-and-down motion of the plane as simple harmonic motion, find(a) the time required for one complete oscillation and (b) the plane’s maximum vertical speed
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.
On December 29, 1997, a United Airlines flight from Tokyo to Honolulu was hit with severe turbulence 31 minutes after
takeoff. Data from the airplane’s “black box” indicated that the 747 moved up and down with an amplitude of 30.0 m
and a maximum acceleration of 1.8g. Treating the up-and-down motion of the plane as
(a) the time required for one complete oscillation and (b) the plane’s maximum vertical speed
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