AP Inter 1st Year Physics Notes Chapter 8 Oscillations

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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. vmax = Aω.

→ The acceleration of the pan Me varies with displacement as, a = -ω2y. The acceleration is zero at the mean position and maximum at the extreme position, amax = Aω2.

→ A simple harmonic motion with amplitude ‘A’ and angular frequency ‘ω’ may be represented as y = A sin (ωt ± Φ0) or y = A cos (ωt ± Φ0).

→ 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) = -ω2A cos (ωt + Φ) = -ω2x(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.