NEET Physics Notes Oscillations-Simple Pendulum
Simple Pendulum
Simple Pendulum
- A simple pendulum, in practice, consists of a heavy but small sized metallic bob suspended by a light, inextensible and flexible string. The motion of a simple pendulum is simple harmonic for very small angular displacement α whose time period and frequency are given by
where, l is the effective length of the string and g is acceleration due to gravity. 
- A second’s pendulum is a pendulum whose time period is 2s. At a place where g = 9.8 ms”2, the length of a second’s pendulum is 0.9929 m (or 1 m approx).
- If a pendulum is in a lift or in some other carriage moving vertically with an acceleration a, then the effective value of the acceleration due to gravity becomes (g ± a) and hence,
- Here, positive sign is taken for an upward accelerated motion and negative sign for a downward accelerated motion.
If a pendulum is made to oscillate in a freely falling lift or an orbiting satellite, then the effective value of g is zero and hence, the time period of the pendulum will be infinity and therefore pendulum will not oscillate at all.
If the pendulum bob of mass m has a charge q and is oscillating in an electrical field E acting vertically downwards then
- If pendulum of charge q is oscillating in an electric field E acting horizontally, then
NOTE
Free, Damped, Forced and Resonant Vibrations
As we know, a periodic motion in which a body moves black and forth repeatedly about a mean position is called oscillatory motion. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but it is sometimes used as a synonym of oscillation. Some of the vibrations are described below.
Free Vibrations
If a body, capable of oscillating is slightly displaced from its position of equilibrium and then released, it starts oscillating with a frequency of its own. Such oscillations are called free vibrations.The frequency with which a body oscillates is called the natural frequency and is given by
Here, a body continues to oscillate with a constant amplitude and a fixed frequency
Damped Vibrations
The oscillations in which the amplitude decreases gradually with the passage of time are called damped vibrations. Damping force, Fd – -bv
where, v is the velocity of the oscillator and b is a damping constant. The displacement of the oscillator is given by 
Forced Vibrations
The vibrations in which a body oscillates under the effect of an external periodic force, whose frequency is different from the natural frequency of the oscillating body, are called forced vibrations. In forced vibrations *the oscillating body vibrates with the frequency of the external force and amplitude of oscillations is generally small.
Resonant Vibrations
It is a special case of forced vibrations in which the frequency of external force is exactly same as the natural frequency of the oscillator. As a result, the oscillating body begins to vibrate with a large amplitude leading to the phenomenon of resonance to occur. Resonant vibrations play a very important role in music and in tuning of station/channel in a radio/TV, etc.