Physics : Oscillations - Summary - Physics: Oscillations

**SUMMARY**

When
an object or a particle moves back and forth repeatedly about a reference point
for some duration of time it is said to have Oscillatory (or vibratory) motion.

For
a SHM, the acceleration or force on the particle is directly proportional to
its displacement from a fixed point and always directed towards that fixed
point. The force is

*F _{x} *= −

where
*k* is a constant whose dimension is
force per unit length, called as force constant.

In Simple harmonic motion, the displacement, *y* = *A*
sin ω*t*.

In Simple harmonic motion, the velocity, *v* = A ω cos ωt = ω√[A^{2}-y^{2}]

In Simple harmonic motion, the acceleration, a =

The time period is defined as the time taken by a
particle to complete one oscillation. It is usually denoted by *T*. Time period *T* =

The number of oscillations produced by the particle
per second is called frequency. It is denoted by *f*. SI unit for frequency is *S*^{−1}
or hertz (In symbol, Hz). Mathematically, frequency is related to time period
by *f* =1/T.

The frequency of the angular harmonic motion is

For *n*
springs connected in series, the effective spring constant in series is

For *n*
springs connected in parallel, the effective spring constant is

The time period for U-tube oscillation is T

For
a conservative system in one dimension, the force field can be derived from a scalar
potential energy: * *

In
a simple harmonic motion, potential energy is *U* ( *x*).

In
a simple harmonic motion, kinetic energy is *KE*.

Total energy for a simple harmonic motion is .

Types
of oscillations – Free oscillations, Damped oscillations, Maintained
oscillations and Forced oscillations.

Resonance
is a special case of forced oscillations.

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11th Physics : Oscillations : Summary - Physics: Oscillations |

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