Oscillations — Class 12 Maharashtra HSC Physics revision notes
A 7-page visual revision sheet for Oscillations, written for Class 12 Maharashtra HSC Physics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Oscillations in one look
one restoring force proportional to displacement, and everything else in this chapter follows from it
Periodic, oscillatory and simple harmonic
- periodic motion repeats after a fixed interval, the period T
- oscillatory motion goes back and forth about a mean position
- every oscillation is periodic, not every periodic motion oscillates (circular motion)
- along a line: linear S.H.M.; along an arc: angular S.H.M.
- frequency n = 1/T, angular frequency ω = 2π n = 2π/T
The defining condition and its equation
- restoring force, always toward the mean position
f = -kx - Newton's second law gives
ma = -kx - the differential equation of linear S.H.M.
d^2x/dt^2 + ω^2x = 0,quad ω^2=k/m
Displacement, velocity and acceleration
- displacement
x = Asin(ω t + φ) - velocity
v = dx/dt = Aωcos(ω t + φ) = ω√A^2-x^2 - acceleration
a = dv/dt = -Aω^2sin(ω t + φ) = -ω^2x
The two extremes of a swing
| mean position, x = 0 | extreme, x = ± A | |
|---|---|---|
| speed | largest, Aω | zero, for an instant |
| acceleration | zero | largest, Aω^2 |
| energy | all kinetic | all potential |
Page 1 of 7. The full sheet, all 7 pages, opens free in the app.
What this Oscillations sheet covers
- periodic motion
- simple harmonic motion
- Periodic, oscillatory and simple harmonic
- The defining condition and its equation
- restoring force, always toward the mean position
- Newton's second law gives
- the differential equation of linear S.H.M.
- Displacement, velocity and acceleration
- displacement
- velocity
- acceleration
- The two extremes of a swing
- S.H.M. as a projection of circular motion
- Period and frequency
- angular frequency, spring-mass system
- period, from acceleration per unit displacement
- frequency
- In the lab: a helical spring
- Springs in combination
- in series, same force f on each spring
- in parallel, same extension on each spring
- Reading the phase
- composition of shm
- Composition of two S.H.M.s, same period and path
- resultant amplitude
- resultant phase
- Three special cases
- Energy in S.H.M.
- Energy formulas
- kinetic energy at displacement x
- potential energy at displacement x
- total energy, any instant
- simple pendulum
- Simple pendulum, the numbers
- period
- angular frequency
- In the lab: the simple pendulum
- In a lift; a physical pendulum
- in a lift, speeding up / down
- a rigid body, G a distance d below the pivot
- Conical pendulum
- Angular S.H.M.
- restoring torque, angular displacement θ
- differential equation, moment of inertia I
- Damped oscillations
- Damped oscillation, the equation
- equation of motion, spring constant k
- the damped angular frequency
- resonance
- Free oscillations, forced oscillations and resonance
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Physics chapter by chapter against your real exam dates and free hours, and when the plan reaches Oscillations the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.
More Physics Class 12 revision notes
- AC Circuits
- Current Electricity
- Dual Nature of Radiation and Matter
- Electromagnetic Induction
- Electrostatics
- Kinetic Theory of Gases and Radiation
- Magnetic Fields due to Electric Current
- Magnetic Materials
- Mechanical Properties of Fluids
- Rotational Dynamics
- Semiconductor Devices
- Structure of Atoms and Nuclei
- Superposition of Waves
- Thermodynamics
- Wave Optics