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 = − k 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 ωt.

In Simple harmonic motion, the velocity, v = A ω cos ωt = ω√[A²-y²]

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 = 2Ï€/ω

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.