The center of oscillation of a physical pendulum has this interesting property: If an impulse (assumed horizontal and in the plane of oscillation) acts at the center of oscillation, no oscillations are felt at the point of support. Baseball players (and players of many other sports) know that unless the ball hits the bat at this point (called the “sweet spot” by athletes), the oscillations due to the impact will sting their hands. To prove this property, let the stick simulate a baseball bat. Suppose that a horizontal force (due to impact with the ball) acts toward the right at P, the center of oscillation. The batter is assumed to hold the bat at O, the pivot point of the stick. (a) What acceleration does the point O undergo as a result of ? (b) What angular acceleration is produced by about the center of mass of the stick? (c) As a result of the angular acceleration in (b), what linear acceleration does point O undergo? (d) Considering the magnitudes and directions of the accelerations in (a) and (c), convince yourself that P is indeed the “sweet spot.”
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.
The center
of oscillation of a
physical pendulum
has this interesting property: If an impulse (assumed horizontal
and in the plane of oscillation) acts at the center of oscillation, no
oscillations are felt at the point of support. Baseball players (and
players of many other sports) know that unless the ball hits the bat
at this point (called the “sweet spot” by athletes), the oscillations
due to the impact will sting their hands. To prove this property, let
the stick simulate a baseball bat. Suppose that a horizontal
force (due to impact with the ball) acts toward the right
at P, the center of oscillation. The batter is assumed to hold the
bat at O, the pivot point of the stick. (a) What acceleration does the
point O undergo as a result of ? (b) What
produced by about the center of mass of the stick? (c) As a result
of the angular acceleration in (b), what linear acceleration
does point O undergo? (d) Considering the magnitudes and directions
of the accelerations in (a) and (c), convince yourself that P is
indeed the “sweet spot.”
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