Oscillations Class 11 Notes Physics Chapter 14 - CBSE
Chapter : 14
What Are Oscillations ?
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Periodic Motion
A motion that repeats itself at regular intervals of time is called periodic motion.
Time Period/frequency
The smallest interval of time after which the motion is repeated is called the 'period'. The number of oscillations/vibrations of motion is called frequency.
Amplitude
The maximum displacement from mean position is called amplitude.
Simple Harmonic Motion
- Equation of SHM
x = A cos(wt + Φ)
x-displacement, A -amplitude (wt + Φ) – phase of the wave
w – angular frequency
Φ - phase constant
- Acceleration during oscillation is
α = – ω2y
- Velocity
$$v =\sqrt{\omega y_{0}^{2} - y^{2}}\\\text{V}_{max} = \omega y_{0}$$
- K.E. in S.H.M.
$$\text{K.E.} =\frac{1}{2}m\omega^{2}(y_{0}^{2} - y^{2})\\(\text{K.E.})_{max} =\frac{1}{2}m\omega^{2}y_{0}^{2}$$
- P.E. in S.H.M.
$$\text{P.E.} =\frac{1}{2}m\omega^{2}y^{2}\\\text{P.E}_{max} =\frac{1}{2}m\omega^{2}y_{0}^{2}$$
- Total energy in S.H.M.
$$\text{T.E.} =\frac{1}{2}m\omega^{2}y_{0}^{2}$$
Time Period Of Various Systems
- Time period of simple pendulum
$$\text{T} =2\pi\sqrt{\bigg(\frac{l}{g}\bigg)}$$
(a) Effective restoring force in spring-mass system
F = – ky
$$\text{Time period, T} = 2\pi\sqrt{\bigg(\frac{m}{k}\bigg)}$$
(b) Two spring-one mass vertical system (series combination)
$$\text{Force constant =}\frac{k_{1}k_{2}}{k_{1} + k_{2}}\\\text{T} = 2\pi\frac{m(k_{1} + k_{2})}{k_{1}k_{2}}$$
(c) Two springs-one mass vertical system (Parallel combination)
k = k1+ k2+ k3
$$\text{T} =2\pi\frac{m}{(k_{1} + k_{2})}$$
(c) Two springs-one mass vertical system (Parallel combination)
k = k1 + k2 + k3
$$\text{T} = 2\pi\frac{m}{(k_{1} + k_{2})} $$
- Oscillations of a liquid column in a U-tube
$$\text{T} = 2\pi\sqrt{\bigg(\frac{h}{g}\bigg)}$$
- Oscillating of a floating object
$$\text{T} = 2\pi\sqrt{\bigg(\frac{\rho l}{dg}\bigg)}$$
- Oscillations of a pith-ball snug-fit in the neck of a bottle containing air
$$\text{T} =\frac{2\pi}{\text{A}}\sqrt{\bigg(\frac{mV}{\text{E}}\bigg)}$$
Motion Of A Simple Pendulum In A Lift
- When the lift is either stationary or moving up or down with constant velocity
$$\text{T} = 2\pi\sqrt{\bigg(\frac{l}{g}\bigg)}$$
- When the lift is moving up with an acceleration a
$$\text{T = 2}\pi\sqrt{\bigg(\frac{l}{\text{g+a}}\bigg)}$$
- When the lift in moving down with an acceleration a < g
$$\text{T = 2}\pi\sqrt{\bigg(\frac{l}{g-a}\bigg)}$$
- When the lift is moving with an acceleration a = g then lift is having a free fall.
