The oscillations of a physical system results from two basic properties namely elasticity and inertia. Let us consider a body displaced from a mean position. The restoring force brings the body to the mean position.

**Dynamics of harmonic
oscillations**

The oscillations of a
physical system results from two basic properties namely elasticity and
inertia. Let us consider a body displaced from a mean position. The restoring
force brings the body to the mean position.

(i)
At extreme position
when the displacement is maximum, velocity is zero. The acceleration becomes
maximum and directed towards the mean position.

(ii)Under the influence of restoring force, the
body comes back to the mean position and overshoots because of negative
velocity gained at the mean position.

(iii) When the displacement is negative maximum, the
velocity becomes zero and the acceleration is maximum in the positive
direction. Hence the body moves towards the mean position. Again when the
displacement is zero in the mean position velocity becomes positive.

(iv)Due to inertia the body overshoots the mean
position once again. This process repeats itself periodically. Hence the system
oscillates.

The restoring force is directly proportional
to the displacement and directed towards the mean position.

(i.e) F α y

F = −ky ??.(1)

where k is the
force constant. It is the force required to give unit displacement. It is
expressed in N m^{−1}.

From Newton?s
second law, F = ma ...(2)

∴ −k y = ma

or a = (k/m) y
??.(3)

From definition
of SHM acceleration a = −ω^{2}y

The acceleration
is directly proportional to the negative of the displacement. Comparing the
above equations we get,

ω =
root(k/m) ??.(4)

Therefore the
period of SHM is

T=2 π / ω = 2 π root(m/k)

T= 2π
root(inertial factor / s pring factor ) ??(5)

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