assing through its center of mass and parallel to the axis passing through its pivot point as Icm. Show that it period is T = 2π q Icm+md2 mvd where d is the distance between the pivot point and the center of mass. (b) Show that the period has a minimum
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.
Consider the physical pendulum of figure 15.17 (shown below).
(a) Represent its moment of inertia about an axis passing
through its center of mass and parallel to the axis passing through its pivot point as Icm. Show that it period
is T = 2π
q
Icm+md2
mvd where d is the distance between the
pivot point and the center of mass.
(b) Show that the period has a minimum value when d satisfies md2 = Icm.
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