⬛ *`Key Points of Chapter Oscillatin
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*1 ➜ Oscillation is the repeated to-and-fro motion about a mean position.*
2 ➔ It occurs when a body moves back and forth repeatedly over the same path.
3 ➜ The motion is said to be periodic if it repeats after regular intervals.
4 ➔ The central (mean) position is the equilibrium point.
5 ➜ Amplitude (A) is the maximum displacement from equilibrium (unit: meter, m).
6 ➔ Time period (T) is the time taken to complete one oscillation (unit: second, s).
7 ➜ Frequency (f) is number of oscillations per second (unit: Hertz, Hz).
8 ➔ Frequency f = 1/T.
9 ➜ Angular frequency (ω) = 2πf = 2π/T (unit: rad/s).
10 ➔ Oscillations are either damped, undamped, forced, or free.
11 ➜ Free oscillation occurs without any external force after initial displacement.
12 ➔ Forced oscillation is due to continuous external periodic force.
13 ➜ Damped oscillation gradually decreases in amplitude due to energy loss.
14 ➔ Simple Harmonic Motion (SHM) is a type of oscillatory motion.
15 ➜ In SHM, acceleration is directly proportional to displacement and directed to mean position.
16 ➔ a ∝ -x or a = -ω²x.
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17 ➜ The negative sign shows restoring nature (towards mean position).
18 ➔ Displacement in SHM: x(t) = A sin(ωt) or A cos(ωt).
19 ➜ Velocity in SHM: v = dx/dt = Aω cos(ωt).
20 ➔ Acceleration: a = d²x/dt² = -Aω² sin(ωt).
21 ➜ Maximum velocity = Aω (unit: m/s).
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22 ➔ Maximum acceleration = Aω² (unit: m/s²).
23 ➜ SHM is a projection of uniform circular motion on a diameter.
24 ➔ Phase shows the position of the particle in SHM.
25 ➜ Phase angle (ϕ) determines initial condition of SHM.
26 ➔ Kinetic Energy in SHM: K.E = ½mω²(A² – x²).
27 ➜ Potential Energy in SHM: P.E = ½mω²x².
28 ➔ Total mechanical energy in SHM = ½mω²A² (constant).
29 ➜ Energy oscillates between K.E and P.E during SHM.
30 ➔ Maximum K.E occurs at mean position.
31 ➜ Maximum P.E occurs at extreme positions.
32 ➔ Time period is independent of amplitude in ideal SHM.
33 ➜ Graph of SHM is sinusoidal (sine or cosine wave).
34 ➔ Velocity is maximum at equilibrium position.
35 ➜ Acceleration is maximum at extreme positions.
36 ➔ Velocity is zero at extreme positions.
37 ➜ Acceleration is zero at mean position.
38 ➔ Simple Pendulum performs SHM for small angles (< 15°).
39 ➜ Time period of simple pendulum: T = 2π√(L/g).
40 ➔ L = length of string, g = gravitational acceleration.
41 ➜ T ∝ √L and T ∝ 1/√g.
42 ➔ Frequency of simple pendulum: f = 1/2π √(g/L).
43 ➜ A longer pendulum has more time period.
44 ➔ On Moon (lower g), pendulum oscillates slowly (higher T).
*45 ➜ In SHM, restoring force: F = -kx.
46 ➔ This restoring force is provided by tension (pendulum) or spring.
47 ➜ Spring-mass system also executes SHM.
48 ➔ For horizontal spring-mass system: T = 2π√(m/k).
49 ➜ m = mass, k = spring constant.
50 ➔ In vertical spring, equilibrium is shifted due to gravity.
51 ➜ Time period of vertical mass-spring: T = 2π√(m/k) (same as horizontal).
52 ➔ Extension due to weight in spring = mg = kx.
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53 ➜ Spring constant k has unit N/m.
54 ➔ Greater the mass, greater the time period.
55 ➜ Greater the spring constant, smaller the time period.
56 ➔ ω = √(k/m) for spring SHM.
57 ➜ Energy in spring SHM: E = ½kA² (constant).
58 ➔ Work done in stretching spring = ½kx².
59 ➜ Resonance is a condition when frequency of driving force = natural frequency.
60 ➔ At resonance, amplitude becomes maximum.
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61 ➜ Resonance occurs in bridges, musical instruments, etc.
62 ➔ Damping is decrease in amplitude with time.
63 ➜ Damping is caused by air resistance, friction, etc.
64 ➔ In critical damping, system returns to mean without oscillating.
65 ➜ In overdamping, system returns slowly.
66 ➔ In underdamping, oscillation continues with decreasing amplitude.
67 ➜ SHM is an ideal case with no damping.
68 ➔ Quality factor (Q) measures sharpness of resonance.
69 ➜ High Q = less damping, sharper resonance.
70 ➔ In oscillation, restoring force always acts opposite to displacement.
71 ➜ Oscillatory motion is periodic but all periodic motions are not oscillatory.
72 ➔ Displacement vs time graph of SHM = sine/cosine curve.
73 ➜ Velocity vs time graph = cosine/sine curve (π/2 phase difference).
74 ➔ Acceleration vs time = negative sine/cosine.
75 ➜ Energy vs time graph = sinusoidal for K.E. and P.E.
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76 ➔ Tension in pendulum varies during motion.
77 ➜ In SHM, system oscillates about stable equilibrium.
78 ➔ Instable equilibrium cannot produce SHM.
79 ➜ Mean position: minimum potential energy.
80 ➔ Damped oscillation graph decays with time.
81 ➜ Amplitude in damped SHM: A(t) = A₀e^(-bt/2m).
82 ➔ b is damping constant (unit: kg/s).
83 ➜ Restoring force: F = -mω²x.
84 ➔ Oscillations in atom’s electrons give rise to electromagnetic waves.
85 ➜ Natural frequency depends on mass and stiffness.
86 ➔ In mechanical oscillators, friction reduces amplitude.
87 ➜ SHM is used in clocks, AC circuits, instruments.
88 ➔ Oscillation involves continuous transformation of energy.
89 ➜ Unit of angular frequency = radian per second (rad/s).
90 ➔ Oscillations are basis for sound, light, quantum systems, etc.Stay connected with us:
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