A uniformly straight rigid bar of mass m and length b is placed in a horizontal position across the top of two identical cylindrical rollers. Axes of the two rollers are a distance 2d apart. If fis the frictional coefficient between the cylinder surface and the bar, show that if the bar is displaced a distance x from its central position, then the net horizontal force on the bar is F =- fmgx/d, and the bar will execute simple harmonic motion with a period of 2√/d/fg.
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.
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