Question 1: Palette 1/57

NEET 2026 MCQ

For a simple pendulum, having time period $T$, the variation of kinetic energy (K.E.) with time $(t)$ is represented by:

A

B

C

D

Question 2: Palette 2/57

NEET 2026 MCQ

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 $=20 \mathrm{~g}$ )

A

$0.2 \mathrm{~m} / \mathrm{s}$

B

$1.41 \mathrm{~m} / \mathrm{s}$

C

$14.1 \mathrm{~m} / \mathrm{s}$

D

$2.0 \mathrm{~m} / \mathrm{s}$

Question 3: Palette 3/57

NEET 2026 MCQ

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 $\pi^2=9.8$, and $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

A

0.75 m

B

1.5 m

C

2 m

D

1 m

Question 4: Palette 4/57

NEET 2026 MCQ

A cylindrical cork of uniform density floats in a liquid of density $\rho_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density $\rho_2$, then the similar oscillation has time period $2 T$. The value of $\rho_2 / \rho_1$ is:

A

1/4

B

4

C

2

D

$1 / 2$

Question 5: Palette 5/57

NEET 2026 MCQ

Consider a spring-mass simple harmonic oscillator in one dimension. The mass of the particle is $m \mathrm{~kg}$ and the spring constant is $k \mathrm{Nm}^{-1}$. At a given instant, the extension of the spring is $x$-meter and the speed of the particle is $v \mathrm{~ms}^{-1}$. On the $x-v$ plane, if the graph of $v$ as a function of $x$ is a circle, then the correct option is:

A

$k=\sqrt{m}$

B

$k=\frac{1}{m}$

C

$k=m$

D

$k=m^2$

Question 6: Palette 6/57

NEET 2025 MCQ

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time $t$. Which one of the following options schematically depicts these changes correctly?

A

B

C

D

Question 7: Palette 7/57

NEET 2025 MCQ

Two identical point masses $P$ and $Q$, suspended from two separate massless springs of spring constants $k_1$ and $k_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio ( $A Q / A_\rho$ ) of the amplitude $A Q$ of mass $Q$ to the amplitude $A_\rho$ of mass $P$ is

A

  $\sqrt{\frac{k_2}{k_1}}$

B

$\sqrt{\frac{k_1}{k_2}}$

C

$\frac{k_2}{k_1}$

D

$\frac{k_1}{k_2}$

Question 8: Palette 8/57

NEET 2024 MCQ

A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement

A

$2 \sqrt{A}$

B

$\frac{A}{2}$

C

$\frac{A}{\sqrt{2}}$

D

$A \sqrt{2}$

Question 9: Palette 9/57

NEET 2024 MCQ

The two-dimensional motion of a particle, described by $\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$ is a/an:

A. parabolic path

B. elliptical path

C. periodic motion

D. simple harmonic motion

Choose the correct answer from the options given below:

A

B, C and D only

B

A, B and C only

C

A, C and D only

D

C and D only

Question 10: Palette 10/57

NEET 2024 MCQ

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

A

5 cm, 2 s

B

5 m, 2 s

C

5 cm, 1 s

D

5 m, 1 s

Question 11: Palette 11/57

NEET 2024 MCQ

If the mass of the bob in a simple pendulum is increased 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:

A

$\sqrt{3}$

B

$\sqrt{2}$

C

$2 \sqrt{3}$

D

4

Question 12: Palette 12/57

NEET 2023 MCQ

A simple pendulum oscillating in air has a period of $\sqrt{3} \mathrm{~s}$. If it is completely immersed in non-viscous liquid, having density $\left(\frac{1}{4}\right)^{\text {th }}$ of the material of the bob, the new period will be :-

A

$2 \sqrt{3}$ s

B

$\frac{2}{\sqrt{3}} \mathrm{~s}$

C

$2 \mathrm{~s}$

D

$\frac{\sqrt{3}}{2} \mathrm{~s}$

Question 13: Palette 13/57

NEET 2023 MCQ

The $x$ - $t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t=2 \mathrm{~s}$ is :

A

$-\frac{\pi^{2}}{8} \mathrm{~ms}^{-2}$

B

$\frac{\pi^{2}}{16} \mathrm{~ms}^{-2}$

C

$-\frac{\pi^{2}}{16} \mathrm{~ms}^{-2}$

D

$\frac{\pi^{2}}{8} \mathrm{~ms}^{-2}$

Question 14: Palette 14/57

NEET 2022 MCQ

Match List-I with List-II

	List-I (x-y graphs)		List-II (Situations)
(a)		(i)	Total mechanical energy is conserved
(b)		(ii)	Bob of a pendulum is oscillating under negligible air friction
(c)		(iii)	Restoring force of a spring
(d)		(iv)	Bob of a pendulum is oscillating along with air friction

Choose the correct answer from the options given below

A

(a) - (iii), (b) - (ii), (c) - (i), (d) - (iv)

B

(a) - (iv), (b) - (ii), (c) - (iii), (d) - (i)

C

(a) - (iv), (b) - (iii), (c) - (ii), (d) - (i)

D

(a) - (i), (b) - (iv), (c) - (iii), (d) - (ii)

Question 15: Palette 15/57

NEET 2022 MCQ

Identify the function which represents a non-periodic motion.

A

$\sin (\omega t + \pi /4)$

B

${e^{ - \omega t}}$

C

$\sin \omega t$

D

$\sin \omega t + \cos \omega t$

Question 16: Palette 16/57

NEET 2022 MCQ

Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :

A

11

B

9

C

10

D

8

Question 17: Palette 17/57

NEET 2021 MCQ

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

A

4n

B

n

C

2n

D

3n

Question 18: Palette 18/57

NEET 2021 MCQ

A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is -

A

0.628 s

B

0.0628 s

C

6.28 s

D

3.14 s

Question 19: Palette 19/57

NEET 2020 MCQ

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

A

${{3\pi } \over 2}rad$

B

${\pi \over 2}rad$

C

zero

D

$\pi $ rad

Question 20: Palette 20/57

NEET 2019 MCQ

The radius of circle, the period of revolution, initial position and sense of revolution are indicated is the figure.

y- projection of the radius vector of rotating particle P is :

A

y(t) = 4sin$\left( {{{\pi t} \over 2}} \right)$, where y in m

B

y(t) = 3cos$\left( {{{3\pi t} \over 2}} \right)$, where y in m

C

y(t) = 3cos$\left( {{{\pi t} \over 2}} \right)$, where y in m

D

y(t) = -3cos2$\pi $t, where y in m

Question 21: Palette 21/57

NEET 2019 MCQ

Average velocity of a particle executing SHM in one complete vibration is :

A

A$\omega $

B

${{A{\omega ^2}} \over 2}$

C

${{A\omega } \over 2}$

D

zero

Question 22: Palette 22/57

NEET 2019 MCQ

The displacement of a particle executing simple harmonic motion is given by

y = A₀ + A sin$\omega $t + B cos$\omega $t.

Then the amplitude of its oscillation is given by :

A

$\sqrt {{A^2} + {B^2}} $

B

A + B

C

A + $\sqrt {{A^2} + {B^2}} $

D

$\sqrt {A_0^2 + {{\left( {A + B} \right)}^2}} $

Question 23: Palette 23/57

NEET 2018 MCQ

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is 20 m s^–2 at a distance of 5 m from the mean position. The time period of oscillation is

A

2$\pi $ s

B

$\pi $ s

C

2 s

D

1 s

Question 24: Palette 24/57

NEET 2017 MCQ

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is K'. Then they are connected in parallel and force constant is k''. Then k' : k'' is

A

1 : 9

B

1 : 11

C

1 : 14

D

1 : 6

Question 25: Palette 25/57

NEET 2017 MCQ

A particle executes linear simple harmonic motion with an amplitude of 3 cm. When the particle is at 2 cm from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in second is

A

${{\sqrt 5 } \over {2\pi }}$

B

${{4\pi } \over {\sqrt 5 }}$

C

${{2\pi } \over {\sqrt 3 }}$

D

${{\sqrt 5 } \over \pi }$

Question 26: Palette 26/57

NEET 2016 MCQ

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 5 s. The value of m in kg is

A

${3 \over 4}$

B

${4 \over 3}$

C

${{16} \over 9}$

D

${9 \over {16}}$

Question 27: Palette 27/57

NEET 2015 MCQ

A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha $ and maximum velocity is $\beta $. Them, its time period of vibration will be

A

${{{\beta ^2}} \over \alpha }$

B

${{2\pi \beta } \over \alpha }$

C

${{{\beta ^2}} \over {{\alpha ^2}}}$

D

${\alpha \over \beta }$

Question 28: Palette 28/57

NEET 2015 MCQ

When two displacements represented by y₁ = a sin${\left( {\omega t} \right)}$ and y₂ = b cos${\left( {\omega t} \right)}$ aresuperimposed the motion is

A

simple harmonic with amplitude $\sqrt {{a^2} + {b^2}} $

B

simple harmonic with amplitude ${{\left( {a + b} \right)} \over 2}$

C

not a simple harmonic

D

simple harmonic with amplitude ${a \over b}$

Question 29: Palette 29/57

NEET 2015 MCQ

A particle is executing SHM along a straight line. Its velocities at distances x₁ and x₂ from the mean position are V₁ and V₂ respectively. Its time period is

A

$2\pi \sqrt {{{V_1^2 + V_2^2} \over {x_1^2 + x_2^2}}} $

B

$2\pi \sqrt {{{V_1^2 - V_2^2} \over {x_1^2 - x_2^2}}} $

C

$2\pi \sqrt {{{x_1^2 + x_2^2} \over {V_1^2 + V_2^2}}} $

D

$2\pi \sqrt {{{x_2^2 - x_1^2} \over {V_1^2 - V_2^2}}} $

Question 30: Palette 30/57

NEET 2014 MCQ

The oscillation of a body on a smooth horizontal surface is represented by the equation,
X = A cos$\left( {\omega t} \right)$
where X = displacement at time t
$\omega $ = frequency of oscillation
Which one of the following graphs shows correctly the variation a with t?
Here a = acceleration at time t
T = time period

A

B

C

D

Question 31: Palette 31/57

NEET 2013 MCQ

A particle of mass m oscillates along x-axis according to equation x = asin$\omega $t. The nature of the graph between momentum and displacement of the particle is

A

Circle

B

Hyperbola

C

Ellipse

D

Straight line passing through origin

Question 32: Palette 32/57

NEET 2011 MCQ

Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is

A

${\pi \over 6}$

B

0

C

${{2\pi } \over 3}$

D

$\pi $

Question 33: Palette 33/57

NEET 2011 MCQ

Out of the following functions representing motion of a particle which represents SHM
(1)  y = sin$\omega $t $-$ cos$\omega $t
(2)  y = sin³$\omega $t
(3)  y = 5cos$\left( {{{3\pi } \over 4} - 3\omega t} \right)$
(4)  y = 1 + $\omega $t + $\omega $²t²

A

Only (1)

B

Only (4) does not represent SHM

C

Only (1) and (3)

D

Only (1) and (2)

Question 34: Palette 34/57

NEET 2010 MCQ

The displacement of a particle along the x-axis is given by x = asin²$\omega $t. The motion of the particle corresponds to

A

simple harmonic motion of frequency $\omega $/$\pi $

B

simple harmonic motion of frequency $3\omega /2\pi $

C

non simple harmonic motion

D

simple harmonic motion of frequency $\omega /2\pi $

Question 35: Palette 35/57

NEET 2010 MCQ

The period of oscillation of a mass M suspended from a strong of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be

A

T

B

${T \over {\sqrt 2 }}$

C

2T

D

$\sqrt 2 T$

Question 36: Palette 36/57

NEET 2009 MCQ

Which one of the following equations of motion represents simple harmonic motion ?

where k, k₀, k₁ and a are all positive.

A

Acceleration = $-$ k (x + a)

B

Acceleration = k(x + a)

C

Acceleration = $-$ $\omega $²x

D

Acceleration = $-$ k₀x + k₁x²

Question 37: Palette 37/57

NEET 2009 MCQ

A simple pendulum performs simple harmonic motion about x = 0 with an amplitude a and time period T. The speed of the pendulum at x = a/2 will be

A

${{\pi a} \over T}$

B

${{3{\pi ^2}a} \over T}$

C

${{\pi a\sqrt 3 } \over T}$

D

${{\pi a\sqrt 3 } \over {2T}}$

Question 38: Palette 38/57

NEET 2008 MCQ

Two simple harmonic motions of angular frequency 100 and 1000 rad s^$-$1 have the same displacement amplitude. The ratio of their maximum acceleration is

A

$1:{10^3}$

B

$1:{10^4}$

C

$1:10$

D

$1:{10^2}$

Question 39: Palette 39/57

NEET 2007 MCQ

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

A

$\pi $

B

0.707 $\pi $

C

zero

D

0.5 $\pi $

Question 40: Palette 40/57

NEET 2007 MCQ

The particle executing simple harmonic motion has a kinetic energy K₀cos²$\omega $t. The maximum values of the potential energy and the total energy are respectively

A

K₀/2 and K₀

B

K₀ and 2K₀

C

K₀ and K₀

D

0 and 2k₀

Question 41: Palette 41/57

NEET 2007 MCQ

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible.

When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s²).

A

10.0 cm

B

any value less than 12.0 cm

C

4.0 cm

D

8.0 cm

Question 42: Palette 42/57

NEET 2007 MCQ

A particle executes simple harmonic oscillation with an amplitude $a$. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is

A

T/8

B

T/12

C

T/2

D

T/4

Question 43: Palette 43/57

NEET 2006 MCQ

A rectangular block of mass m and area of cross-section A floats in a liquid of density $\rho $. If it is given a small vertical displacement from equilibrium it undergoes with a time period T, then

A

$T \propto {1 \over {\sqrt m }}$

B

$T \propto \sqrt \rho $

C

$T \propto {1 \over {\sqrt A }}$

D

$T \propto {1 \over \rho }$

Question 44: Palette 44/57

NEET 2005 MCQ

The circular motion of a particle with constant speed is

A

periodic but not simple harmonic

B

simple harmonic but not periodic

C

period and simple harmonic

D

neither periodic not simple harmonic.

Question 45: Palette 45/57

NEET 2004 MCQ

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

A

4 Hz

B

3 Hz

C

2 Hz

D

1 Hz

Question 46: Palette 46/57

NEET 2004 MCQ

Two springs of spring constants k₁ and k₂ are joined in series. The effective spring constant of the combination is given by

A

$\sqrt {{k_1}{k_2}} $

B

(k₁ + k₂)/2

C

k₁ + k₂

D

k₁k₂/(k₁ + k₂)

Question 47: Palette 47/57

NEET 2003 MCQ

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is

A

${2 \over 3}$E

B

${1 \over 8}$E

C

${1 \over 4}$E

D

${1 \over 2}$E

Question 48: Palette 48/57

NEET 2003 MCQ

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

A

T/4

B

T

C

T/2

D

2T

Question 49: Palette 49/57

NEET 2003 MCQ

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?

A

When v is maximum, $a$ is maximum

B

Value of $a$ is zero, whatever may be the value of v.

C

When v is zero, $a$ is zero

D

When v is maximum, $a$ is zero.

Question 50: Palette 50/57

NEET 2003 MCQ

A particle of mass m oscillates with simple harmonic motion between points x₁ and x₂, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph

A

B

C

D

Question 51: Palette 51/57

NEET 2003 MCQ

In case of a forced vibration, the resonance peak becomes very sharp when the

A

damping force is small

B

restoring force is small

C

applied periodic force is small

D

quality factor is small

Question 52: Palette 52/57

NEET 2002 MCQ

Displacement between maximum potential energy position and maximum kinetic energy position for a particle executing simple harmonic motion is

A

$ \pm $ $a$/2

B

+ $a$

C

$ \pm $ $a$

D

$-$ 1

Question 53: Palette 53/57

NEET 2002 MCQ

When an oscillator completes 100 oscillations its amplitude reduced to ${1 \over 3}$ of initial value. What will be its amplitude, when it complettes 200 oscillations ?

A

${1 \over 8}$

B

${2 \over 3}$

C

${1 \over 6}$

D

${1 \over 9}$

Question 54: Palette 54/57

NEET 2002 MCQ

A mass is suspended separately by two different springs in (successive order then time periods is t₁ and t₂ respectively, If it is connected by both spring as shown in figure then time period is t₀ , the correct relation is

A

$t_0^2 = t_1^2 + t_2^2$

B

$t_0^{ - 2} = t_1^{ - 2} + t_2^{ - 2}$

C

$t_0^{ - 1} = t_1^{ - 1} + t_2^{ - 1}$

D

${t_0} = {t_1} + {t_2}$

Question 55: Palette 55/57

NEET 2001 MCQ

The total energy of particle performing SHM depend on

A

k, a, m

B

k, a

C

k, a, x

D

k, x

Question 56: Palette 56/57

NEET 2000 MCQ

Two masses $M$_A and $M$_B are hung from two strings of length $l$_A and $l$_B respectively. They are executing SHM with frequency relation $f$_A = 2$f$_B, then relation

A

${l_A} = {{{l_B}} \over 4}$ does not depend on mass

B

${l_A} = 4{l_B}$, does not depend on mass

C

${l_A} = 2{l_B}$ and ${M_A} = 2{M_B}$

D

${l_A} = {{{l_B}} \over 2}$ and ${M_A} = {{{M_B}} \over 2}$.

Question 57: Palette 57/57

NEET 2000 MCQ

The bob of simple pendulum having length $l$, is displaced from mean position to an angular position q with respect to vertical. If it is released, then velocity of bob at equilibrium position

A

$\sqrt {2gl\left( {1 - \cos \theta } \right)} $

B

$\sqrt {2gl\left( {1 + \cos \theta } \right)} $

C

$\sqrt {2gl\cos \theta } $

D

$\sqrt {2gl} $