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.