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. 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.