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Why is the formula for period of simple harmonic motion independent of amplitude?
Simple harmonic motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point with a constant amplitude and a sinusoidal displacement over time.
The period of simple harmonic motion is the time it takes for one complete cycle of oscillation, from one point of maximum displacement to the next. It is denoted by the symbol T and is measured in seconds.
The period of simple harmonic motion is independent of the amplitude. This means that no matter how large or small the amplitude of the oscillation is, the period remains the same as long as the restoring force and mass are constant.
The period of simple harmonic motion can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant of the restoring force.
The period of simple harmonic motion can be changed by altering the mass or the spring constant. A larger mass or a stiffer spring will result in a longer period, while a smaller mass or a less stiff spring will result in a shorter period.