Students can go through AP Inter 1st Year Physics Notes 8th Lesson Oscillations will help students in revising the entire concepts quickly.

## AP Inter 1st Year Physics Notes 8th Lesson Oscillations

→ If a body repeats its motion at regular intervals of time, the motion is said to be periodic.

→ If a body moves to and fro about a fixed point in its path and if the acceleration is proportional to the displacement of the body from a fixed point and directed towards the fixed point, then the motion of the body is called simple harmonic motion.

→ One complete to and fro motion of a body is called an oscillation or vibration.

→ The time required for one oscillation of a body is called its period of oscillation.

→ The maximum displacement of a vibrating body from the rest position is called its amplitude.

→ The number of vibrations made by a body in unit time is called its frequency.

→ The phase of vibration of a particle is the state of motion related to the time with reference to the average position of rest.

→ The force constant of a system is equal to the force to be applied on the particle to cause unit displacement.

→ The time taken for one complete oscillation is known as the time period of simple harmonic motion given by T = \(\frac{2 \pi}{\omega}\)

→ The number of oscillations per second is known as the frequency (i.e., υ = \(\frac{1}{T}\) )

→ The velocity of the particle in SHM varies with displacement ‘y’ given by v = ω \(\sqrt{A^2-y^2}\)

→ The velocity is equal to zero at the extreme position and maximum at the mean position. v_{max} = Aω.

→ The acceleration of the pan Me varies with displacement as, a = -ω^{2}y. The acceleration is zero at the mean position and maximum at the extreme position, a_{max} = Aω^{2}.

→ A simple harmonic motion with amplitude ‘A’ and angular frequency ‘ω’ may be represented as y = A sin (ωt ± Φ_{0}) or y = A cos (ωt ± Φ_{0}).

→ A simple pendulum of length ‘l’ makes simple harmonic oscillations with small amplitudes. The period of oscillation is given by T = 2π \(\sqrt{\frac{l}{g}}\).

→ The time period of a loaded spring is T = 2π \(\sqrt{\frac{m}{K}}\) where K is force constant.

→ The particle velocity and acceleration during SHM as a function of time are given by

v(t) = -ωA sin (ωt + Φ)

a(t) = -ω^{2}A cos (ωt + Φ) = -ω^{2}x(t)

→ The damped simple harmonic motion is not strictly simple harmonic.

→ In an ideal case of zero damping, the amplitude of SHM at resonance is infinite.

→ Under forced oscillation, phase of harmonic motion of the particle differs from the phase of the driving force.

→ The phenomenon of increase in amplitude when the driving force is close of the natural frequency of the oscillator is called resonance.