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NEET Physics Notes Oscillations-Terms Related to SHM

NEET Physics Notes Oscillations-Terms Related to SHM

Terms Related to SHM

The few important terms related to simple harmonic motion are given as

Displacement

The displacement of a particle executing SHM is, in general, expressed as
NEET Physics Notes Oscillations-Terms Related to SHM 1
where, A is the amplitude of SHM
ω the angular frequency NEET Physics Notes Oscillations-Terms Related to SHM 2
Φ is the initial phase of SHM.
However, displacement may also be expressed as
NEET Physics Notes Oscillations-Terms Related to SHM 3

Velocity

The velocity of a particle executing SHM at an instant is defined as the time rate of change of its displacement at that instant. Velocity, NEET Physics Notes Oscillations-Terms Related to SHM 4
At the mean position (y = 0), during its motion NEET Physics Notes Oscillations-Terms Related to SHM 5 and at the extreme positions
NEET Physics Notes Oscillations-Terms Related to SHM 6

Acceleration

The acceleration of a particle executing SHM at an instant is defined as the time rate of change of velocity at that instant. Acceleration, NEET Physics Notes Oscillations-Terms Related to SHM 7
The acceleration is also a variable. At the mean position (y = 0), acceleration a = 0 and at the extreme position (y = ± A), the acceleration is NEET Physics Notes Oscillations-Terms Related to SHM 8
NEET Physics Notes Oscillations-Terms Related to SHM 9

Phase and It’s Relationship

Phase is that physical quantity which tells about the position and direction of motion of any particle at any moment. It is denoted by Φ In SHM, the velocity
is ahead of the displacement by a phase \frac{\pi}{2} and the acceleration is further ahead of the velocity by a phase of \frac{\pi}{2}

Time Period

The time taken by a particle to complete one oscillation is called time period. It is denoted by T.
NEET Physics Notes Oscillations-Terms Related to SHM 10

Oscillations of a Spring

A spring pendulum consists of a point (small sized) mass m either suspended from a massless (or light) spring or placed on a smooth horizontal plane attached with a spring.
NEET Physics Notes Oscillations-Terms Related to SHM 11
If the mass is once pulled, so as to stretch the spring and is then released, then a restoring force acts on it which continuously tries to restore its mean position, restoring force F = – kl, where k is force constant and 1 is the change in length of the spring under the restoring force the spring pendulum oscillates simple harmonically having time period and frequency given by

NEET Physics Notes Oscillations-Terms Related to SHM 12
If the spring is not light but has a mass ms, then
NEET Physics Notes Oscillations-Terms Related to SHM 13
If two masses m1 and m2, connected by a spring, are made to oscillate on a horizontal surface, then its
NEET Physics Notes Oscillations-Terms Related to SHM 14

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