NEET PhysicsUpdated 19 Oct 2026

Oscillations: NEET PYQs and weightage

Oscillations carries 3.0 of 100 Physics marks in NEET by past-paper share: 23 of the 758 tagged NEET Physics PYQs in the ViJEEta bank (NEET 2013–2026). It ranks 16 of 30 Physics chapters.

Take the 25-question Oscillations test Formula sheet ↓All NEET Physics chapters

3.0/100 Weight in Physics

Exam importance (3/5, by past-paper share)

23 NEET PYQs

324 Practice questions

303 With measured difficulty

How the weight is computed: this chapter's tagged NEET PYQs divided by all tagged NEET Physics PYQs in the bank (23 of 758), times 100, with repeated questions counted once. The bank does not store the year of each NEET question, so none is printed. Computed from the bank at build time. Updated 19 Oct 2026.

Oscillations: formula sheet for NEET

14 formulas, each with when to use it. Copy it onto one page of your notebook: that page is this chapter's handbook.

Displacement in SHM
$x = A cos (ω t + ϕ)$
Use it when: You need the position at a given time; $A$ = amplitude, $(ω t + ϕ)$ = phase, $ϕ$ = phase at $t = 0$ .
Angular frequency, period, frequency
$ω = \frac{2 π}{T} = 2 π ν$
$ν = \frac{1}{T}$
Use it when: Converting between $ω$ , $T$ and $ν$ ; $ω$ is in rad/s and $ν$ is in Hz, so keep the $2 π$ between them.
Velocity
$v = - ω A sin (ω t + ϕ)$
$v_{m a x} = ω A (at x = 0)$
Use it when: Speed at a time $t$ is asked; $v$ leads $x$ by $π /2$ and $a$ is $π$ out of phase with $x$ .
Speed at a position
$v = ω A^{2} - x^{2}$
Use it when: $x$ is given instead of $t$ (it comes from $\frac{1}{2} m v^{2} + \frac{1}{2} k x^{2} = \frac{1}{2} k A^{2}$ ).
Acceleration
$a = - ω^{2} x$
$a_{m a x} = ω^{2} A (at x = \pm A)$
Use it when: Checking whether a motion is SHM; $a = - (constant) \cdot x$ means SHM with $ω = constant$ .
Restoring force
$F = - k x$
$k = m ω^{2}$
Use it when: You need the force at a displacement, or need $ω$ from a force law ( $ω = k / m$ ).
Spring–block oscillator
$ω = \frac{k}{m}$
$T = 2 π \frac{m}{k}$
Use it when: A mass oscillates on an ideal spring; $T$ does not depend on amplitude.
Simple pendulum
$T = 2 π \frac{L}{g} (small θ)$
Use it when: A point bob swings through small angles; only $L$ and $g$ matter, not the mass or the amplitude.
Physical pendulum
$T = 2 π \frac{I}{m g d}$
Use it when: A rigid body swings about an axis; $d$ = distance from the axis to the centre of gravity, $I$ = moment of inertia about that axis.
Energy
$K = \frac{1}{2} k A^{2} sin^{2} (ω t + ϕ)$
$U = \frac{1}{2} k x^{2}$
$E = K + U = \frac{1}{2} k A^{2} = \frac{1}{2} m ω^{2} A^{2}$
Use it when: Splitting energy at any $x$ or $t$ ; $E$ stays constant, all of it is $K$ at $x = 0$ and all of it is $U$ at $x = \pm A$ .
Block between two identical springs
$T = 2 π \frac{m}{2 k} (each spring k)$
Use it when: One spring pulls and the other pushes, so the effective constant is $2 k$ .
Angular SHM (torsion)
$ω = \frac{κ}{I}$
$f = \frac{1}{2 π} \frac{κ}{I}$
Use it when: A body such as a balance wheel twists back and forth under a restoring torque; $κ$ = torsion constant.
Floating cylinder pressed and released
$T = 2 π \frac{h ρ}{ρ _{l} g}$
Use it when: A cork of height $h$ and density $ρ$ bobs in a liquid of density $ρ_{l}$ .
Damped oscillation
$x = A e^{- b t /2 m} cos (ω^{'} t + ϕ)$
$ω^{'} = \frac{k}{m} - \frac{b ^{2}}{4 m ^{2}}$
Use it when: A drag force $- b v$ acts and $b < 2 k m$ (underdamping); the amplitude decays and $ω^{'} < k / m$ . At $b = 2 k m$ (critical) or $b > 2 k m$ (overdamped) the body returns to equilibrium without oscillating.

Trap

K and U each repeat every T/2, so each oscillates at frequency 2ν while E = K + U stays constant. Students often give the period of K or U as T.

How does NEET ask Oscillations?

8 real previous-year questions from this chapter, as printed in the paper, each with its worked solution. Answer the first one here with no sign-in.

Q1PhysicsNEET UG PYQSimple Pendulum

Try right here · No sign-in

If the mass of the bob in a simple pendulum increases to thrice its original mass and its length is made half its original length, then the new time period of oscillation is

\frac{x}{2}

times its original time period. Then the value of x is

Answer key (A) & worked solution

Correct answer: Option A

T = 2 π \frac{L}{g}

\frac{T}{T ^{'}} = \frac{L}{L /2} = 2 \Rightarrow T^{'} = \frac{T}{2}

But

T^{'} = \frac{x}{2} T

\frac{x}{2} = \frac{1}{2}

x = 2

Q2PhysicsNEET UG PYQEnergy in Simple Harmonic Motion

A body is executing simple harmonic motion with frequency ‘n’, the frequency of its potential energy is:

A3n

B4n

D2n

Answer key (D) & worked solution

Correct answer: Option D

Displacement equation of SHM of frequency 'n'

x = A sin (ω t) = A sin (2 π n t)

Now,Potential energy

U = \frac{1}{2} kx^{2} = \frac{1}{2} KA^{2} sin^{2} (2 π nt)

= \frac{1}{2} k A^{2} [\frac{1 - cos ( 2 π ( 2 n ) t )}{2}]

So frequency of potential energy

= 2 n

Q3PhysicsNEET UG PYQVelocity and Acceleration in SHM

The phase difference between the displacement and acceleration of a particle in a simple harmonic motion is:

\frac{π}{2} r a d

Bzero

π r a d

\frac{3 π}{2} r a d

Answer key (C) & worked solution

Correct answer: Option C

for SHM acceleration and displacement both must have opposite direction

a = - ω^{2} x ∴

phase diff. is

π

∴ x = A sin (ω t)

a = - A ω^{2} sin ω t

Q4PhysicsNEET UG PYQForce Law for SHM

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is

\frac{4}{3}

\frac{16}{9}

\frac{9}{16}

\frac{3}{4}

Answer key (C) & worked solution

Correct answer: Option C

T = 2 π \frac{m}{k}

3 = 2 π \frac{m}{k}

… (1)

5 = 2 π \frac{m + 1}{k}

… (2)

\frac{( 1 ) ^{2}}{( 2 ) ^{2}} \Rightarrow \frac{9}{25} = \frac{m}{m + 1} \Rightarrow m = \frac{9}{16}

Q5PhysicsNEET UG PYQEnergy in Simple Harmonic Motion

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is

m kg

and the spring constant is

k Nm^{- 1}

. At a given instant, the extension of the spring is

x

-meter and the speed of the particle is

v ms^{- 1}

. On the

x - v

plane, if the graph of

v

as a function of

x

is a circle, then the correct option is:

k = m

k = m^{2}

k = m

k = \frac{1}{m}

Answer key (A) & worked solution

Correct answer: Option A

Velocity

v

as a function of

n

is given by

v = ω A^{2} - X^{2}

v^{2} = ω^{2} (A^{2} - x^{2})

\frac{v ^{2}}{ω ^{2}} + x^{2} = A^{2}

Given that above equation is of a circle Hence,

ω^{2} = 1

\frac{k}{m} = 1

k = m

Q6PhysicsNEET UG PYQEnergy in Simple Harmonic Motion

The sum of kinetic energy and potential energy of a simple pendulum bob is 0.02 joule. The speed of the simple pendulum bob at equilibrium position is approximately: (Consider mass of the bob

= 20 g

)

1.41 m / s

14.1 m / s

0.2 m / s

2.0 m / s

Answer key (A) & worked solution

Correct answer: Option A

At equilibrium position Total energy = K.E

\frac{1}{2} m v^{2} = 0.02

\frac{1}{2} \times 20 \times v^{2} \times 1 0^{- 3} = 2 \times 1 0^{- 2}

v = 2

v = 1.41 m / s

Q7PhysicsNEET UG PYQVelocity and Acceleration in SHM

A particle is executing SHM along a straight line. Its velocities at distances

x_{1}

and

x_{2}

, from the mean position are

v_{1}

and

v_{2}

, respectively. Its time period is:

2 π \frac{v _{1}^{2} - v _{2}^{2}}{x _{1}^{2} - x _{2}^{2}}

2 π \frac{x _{1}^{2} + x _{2}^{2}}{v _{1}^{2} + v _{2}^{2}}

2 π \frac{x _{2}^{2} - x _{1}^{2}}{v _{1}^{2} - v _{2}^{2}}

2 π \frac{v _{1}^{2} + v _{2}^{2}}{x _{1}^{2} + x _{2}^{2}}

Answer key (C) & worked solution

Correct answer: Option C

V_{1} = ω A^{2} - x_{1}^{2} ∴ v_{1}^{2} = ω^{2} (A^{2} - x_{1}^{2})

v_{2} = ω A^{2} - x_{2}^{2} ∴ v_{2}^{2} = ω^{2} (A^{2} - x_{2}^{2})

∴ v_{1}^{2} - v_{2}^{2} = ω^{2} (x_{2}^{2} - x_{1}^{2})

∴ ω^{2} = \frac{v _{1}^{2} - v _{2}^{2}}{x _{2}^{2} - x _{1}^{2}}

∴ ω = \frac{v _{1}^{2} - v _{2}^{2}}{x _{2}^{2} - x _{1}^{2}} ∴ T = \frac{2 π}{ω} = 2 π \frac{x _{2}^{2} - x _{1}^{2}}{v _{1}^{2} - v _{2}^{2}}

Q8PhysicsNEET UG PYQSimple Pendulum

Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum

L

, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as : (Take

π^{2} = 9.8

, and

g = 9.8 m / s^{2}

)

A2 m

B0.75 m

C1.5 m

D1 m

Answer key (D) & worked solution

Correct answer: Option D

Time taken for 30 oscillations

= 60 s

Time period of simple pendulum = Time taken for 1 oscillation

\Rightarrow T = \frac{60}{30} = 2 s T = 2 π \frac{l}{g} \Rightarrow l = \frac{g T ^{2}}{4 π ^{2}} = \frac{9.8 \times 2 \times 2}{4 \times 9.8} = 1 m

Which topics in Oscillations carry the most questions?

All 7 topics, by tagged PYQs, then practice questions. Counted from the bank. Updated 19 Oct 2026.

Topic	PYQs	Practice questions
Simple Harmonic Motion	9	115
Energy in Simple Harmonic Motion	4	65
Force Law for SHM	4	36
Simple Pendulum	3	56
Velocity and Acceleration in SHM	3	43
Period and Frequency	0	5
Miscellaneous Examples	0	4

Why does Oscillations show "–" until you answer 3 questions?

Unknown is not zero. Until you answer at least 3 graded questions in Oscillations, ViJEEta shows – instead of a zero or a 50% default. Book exercises can raise chapter mastery up to 0.60, adaptive practice up to 0.75, and only a timed chapter test or mock can certify 0.80 and above.

How ViJEEta scores you

What happens when you test Oscillations?

Every chapter test is 25 questions. It starts at moderate difficulty and adapts after each saved answer. If you open a solution before answering, that attempt earns no credit, so your mastery stays honest.

Start the Oscillations test

Chapters either side of Oscillations by weight

Units and Measurement Weight 3.2/100 Atoms Weight 3.0/100 Mechanical Properties of Fluids Weight 2.9/100 Nuclei Weight 2.9/100

Oscillations: NEET PYQs and weightage

Oscillations: formula sheet for NEET

Displacement in SHM

Angular frequency, period, frequency

Velocity

Speed at a position

Acceleration

Restoring force

Spring–block oscillator

Simple pendulum

Physical pendulum

Energy

Block between two identical springs

Angular SHM (torsion)

Floating cylinder pressed and released

Damped oscillation

How does NEET ask Oscillations?

Which topics in Oscillations carry the most questions?

Why does Oscillations show "–" until you answer 3 questions?

What happens when you test Oscillations?

Chapters either side of Oscillations by weight