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Show that the oscillation of the loaded sping is Simple Harmonic
A particle is said to be simple harmonic motion if its acceleration is directly proportional to the displacement from a fixed point and is always directed towards that point.
Horizontal and vertical oscillations of a loaded spring are some examples of simple harmonic motion.
The blockspring system is a linear simple harmonic oscillator .All oscillating systems like diving board,violin string have some element of springiness, k(spring constant) and some element of inertia,m.
Simple Harmonic Motion horizontal Oscillations of Spring:
Consider a mass(m) attached to an end of a spiral spring(whcih obey's Hooke's law) whose other end is fixed to a support as shown in figure.
The body is placed on a smooth horizontal surface. Let the body be displaced through a distance x towards right and released. It oscillates about its mean position, The restoring force acts in the opposite direction and it is proportional to the displacement.
Restoring force F = kx
From Newton's second law, F= ma
ma = kx
a = x
Comparing with the equation of simple harmonic motion a =  ^{2}x
But time period T =
Time period T =
Frequency =