NDA Physics · Formula sheet

Oscillations and Waves formulas

5 formulas and 12 common traps for NDA Physics Oscillations and Waves, grouped by subtopic.

Simple Harmonic Motion and General Waves

What makes a motion simple-harmonic

Defining condition of SHM

F = -kx \qquad a = -\omega^2 x

$F$ restoring force
$x$ displacement from the mean position
$k$ force constant (positive)
$\omega$ angular frequency

Period, frequency, and phase

Period, frequency, angular frequency

f = \dfrac{1}{T} \qquad \omega = 2\pi f = \dfrac{2\pi}{T}

$T$ period (s)
$f$ frequency (Hz)
$\omega$ angular frequency (rad/s)

Common traps

Acceleration in SHM is NOT constant

A distractor claims the oscillator's acceleration is constant. It is not —

a = -\omega^2 x

changes continuously, peaking at the extremes and vanishing at the mean position. Only the angular frequency

\omega

is constant.

The restoring force opposes the displacement

The force is proportional to displacement and in the OPPOSITE direction (toward the mean position). An option saying 'force in the same direction as displacement' describes an unstable push-away, not SHM.

Motion repeats after EVERY nT, not 'only once' after T

A favourite NDA distractor states 'the motion repeats after time T only once'. False — T is the LEAST repeat time, but the motion also repeats after 2T, 3T, … i.e. after every nT. The 'only once' wording is the wrong statement to pick when asked which is NOT correct.

Same phase needs Δt = nT — count whole periods

Reading a displacement-time graph, two instants are in phase only if their separation is an integer multiple of the period. Δt = T/2 gives equal displacement but OPPOSITE direction of motion — that is anti-phase, not the same phase.

Sound and water waves cannot cross a vacuum — only light can

The statement 'they can travel in vacuum' is true for electromagnetic waves but FALSE for sound and water waves. When a question groups all three wave types, the vacuum-travel option must be excluded — it is the trap that turns '1, 2, 3 and 4' into the wrong answer.

Lightning before thunder = light is faster, not 'sound is slower than expected'

Seeing a flash before hearing the thunder shows light (~3×10⁸ m/s) outruns sound (~343 m/s) over the same distance. The conclusion is about the SPEED difference, not about the brightness or the intensity of the flash.

The Simple Pendulum

Learn this subtopic in the notes

The pendulum period law T = 2π√(L/g) — mass-independent

Period of a simple pendulum

T = 2\pi\sqrt{\dfrac{L}{g}}

$T$ period (s)
$L$ length of the string
$g$ acceleration due to gravity

How gravity changes the period

Period and gravity (length fixed)

\dfrac{T_2}{T_1} = \sqrt{\dfrac{g_1}{g_2}}

$T_1, T_2$ old and new periods
$g_1, g_2$ old and new gravitational accelerations

Amplitude-independence holds only for small swings

Restoring force and the small-angle condition

F = -mg\sin\theta \;\approx\; -mg\,\theta \quad (\theta \text{ small})

$F$ restoring force along the arc
$\theta$ angular displacement from the vertical
$m$ mass of the bob

Common traps

Period does NOT depend on the mass of the bob

Every length-and-mass problem in this bank plants a mass change to distract you.

T = 2\pi\sqrt{L/g}

has no

m

in it — double, triple or halve the mass and the period is unchanged. Read off only what happens to the LENGTH.

Period scales as √L, not as L

Quadrupling the length doubles the period (

\sqrt{4} = 2

), it does NOT quadruple it. A distractor that gives '4T' for a ×4 length is using the wrong power — the square root is the whole point.

Smaller g gives a LONGER period (and a slow clock)

Because

T \propto 1/\sqrt{g}

, weaker gravity LENGTHENS the period — the clock loses time. Don't let the mass in the problem mislead you: the bob's mass never enters, only the change in g (and length) does.

Use the √(g₁/g₂) ratio, not g₁/g₂

Halving g multiplies the period by √2, not by 2. Gravity sits under a square root, so always take the square root of the gravity ratio when comparing periods.

Amplitude-independence is a SMALL-angle property

The period is independent of amplitude only while the swing is small, because only then is sinθ ≈ θ and the restoring force proportional to displacement. At a large amplitude the period is no longer constant — it grows. Picking 'for any amplitude' is the trap.

Large amplitude → period gets LONGER, not shorter

Because sinθ < θ for large angles, the restoring force is weaker than the SHM value, so the bob moves more slowly and the period exceeds T₀. An option saying the large-angle period is slightly SMALLER than T₀ has the inequality backwards.

Oscillations and Waves formulas

Simple Harmonic Motion and General Waves

What makes a motion simple-harmonic

Period, frequency, and phase

Common traps

The Simple Pendulum

The pendulum period law T = 2π√(L/g) — mass-independent

How gravity changes the period

Amplitude-independence holds only for small swings

Common traps

More NDA Physics formula sheets