OSCILLATIONS-Objective Questions for Entrance Exams
The chapter “Oscillations” forms one of the most fundamental pillars of classical mechanics and plays a decisive role in developing a student’s conceptual and mathematical understanding of periodic motion. From the idealized motion of a mass–spring system to the real-world behavior of pendulums and vibrating systems, oscillatory motion bridges theoretical physics with practical applications across engineering, electronics, and modern technology. Competitive examinations such as JEE (Main & Advanced), NEET, AIIMS, BITSAT, KVPY, Olympiads, and state engineering entrance tests consistently emphasize this chapter due to its strong linkage with waves, thermodynamics, and modern physics.
The present collection of 50 carefully curated multiple-choice questions has been designed to reflect authentic examination patterns, recurring conceptual traps, and frequently tested derivations. Each question is accompanied by a precise answer and a concept-driven explanation to reinforce clarity and exam readiness. The progression of questions ensures coverage from foundational definitions—such as displacement, phase, and angular frequency—to advanced analytical reasoning involving energy distribution, time period dependencies, and phase relationships. These MCQs not only strengthen problem-solving speed but also sharpen conceptual accuracy, making them an indispensable practice resource for aspirants targeting high-rank performance in physics-intensive competitive examinations.
Actual questions from IIT-JEE, NEET, AIIMS, BITSAT & KVPY —
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Q1
The displacement of a particle executing SHM is given by \(x = A\sin(\omega t)\). The maximum velocity of the particle is (Exam: IIT-JEE Year: 1998)
(A) \(A\omega\)
(B) \(A/\omega\)
(C) \(\omega/A\)
(D) \(A^2\omega\)
✅ Correct: (A)
Q2
The time period of a simple pendulum depends on (Exam: NEET Year: 2005)
(A) mass of the bob
(B) amplitude of oscillation
(C) length of the pendulum
(D) material of the string
✅ Correct: (C)
Q3
In SHM, acceleration is proportional to (Exam: CBSE Year: 2008)
(A) velocity
(B) displacement
(C) square of displacement
(D) time
✅ Correct: (B)
Q4
The total energy of a particle executing SHM is (Exam: AIIMS Year: 2010)
(A) maximum at mean position
(B) minimum at extreme position
(C) constant throughout motion
(D) zero at mean position
✅ Correct: (C)
Q5
The phase difference between displacement and velocity in SHM is (Exam: JEE Main Year: 2013)
(A) \(0\)
(B) \(\pi/2\)
(C) \(\pi\)
(D) \(3\pi/2\)
✅ Correct: (B)
Q6
For a mass-spring system, the angular frequency is (Exam: BITSAT Year: 2014)
(A) \(\sqrt{mk}\)
(B) \(\sqrt{k/m}\)
(C) \(k/m\)
(D) \(m/k\)
✅ Correct: (B)
Q7
At the extreme position of SHM, the kinetic energy is (Exam: NEET Year: 2016)
(A) maximum
(B) minimum
(C) zero
(D) equal to potential energy
✅ Correct: (C)
Q8
The restoring force in SHM always acts (Exam: IIT-JEE Year: 2002)
(A) along velocity
(B) opposite to displacement
(C) perpendicular to motion
(D) along displacement
✅ Correct: (B)
Q9
The time period of SHM is independent of (Exam: KVPY Year: 2011)
(A) mass
(B) force constant
(C) amplitude
(D) system type
✅ Correct: (C)
Q10
The unit of angular frequency is (Exam: CBSE Year: 2006)
(A) Hz
(B) rad/s
(C) s
(D) m/s
✅ Correct: (B)
Q11
If the length of a pendulum is doubled, its time period becomes (Exam: NEET Year: 2017)
(A) half
(B) double
(C) \(\sqrt{2}\) times
(D) \(1/\sqrt{2}\) times
✅ Correct: (C)
Q12
In SHM, the potential energy is maximum at (Exam: JEE Main Year: 2014)
(A) mean position
(B) extreme positions
(C) midway
(D) everywhere same
✅ Correct: (B)
Q13
The phase of SHM at \(t=0\) is called (Exam: Olympiad Year: 2012)
(A) final phase
(B) angular frequency
(C) initial phase
(D) time period
✅ Correct: (C)
Q14
The relation between linear frequency \(f\) and angular frequency \(\omega\) is (Exam: CBSE Year: 2009)
(A) \(\omega = f\)
(B) \(\omega = 2\pi f\)
(C) \(f = 2\pi \omega\)
(D) \(f = \omega^2\)
✅ Correct: (B)
Q15
The acceleration of a particle in SHM is zero at (Exam: NEET Year: 2018)
(A) extreme position
(B) mean position
(C) midway
(D) everywhere
✅ Correct: (B)
Q16
The time period of a mass-spring system increases if (Exam: IIT-JEE Year: 2004)
(A) mass is increased
(B) spring constant is increased
(C) amplitude is increased
(D) gravity is increased
✅ Correct: (A)
Q17
In SHM, velocity is maximum at (Exam: BITSAT Year: 2015)
(A) extreme position
(B) mean position
(C) midway
(D) everywhere
✅ Correct: (B)
Q18
The energy of SHM is proportional to (Exam: KVPY Year: 2010)
(A) amplitude
(B) square of amplitude
(C) time period
(D) frequency
✅ Correct: (B)
Q19
A particle executes SHM with period \(T\). The time taken to go from mean to extreme position is (Exam: JEE Main Year: 2016)
(A) \(T/2\)
(B) \(T/4\)
(C) \(T/8\)
(D) \(T\)
✅ Correct: (B)
Q20
The dimension of spring constant \(k\) is (Exam: CBSE Year: 2011)
(A) \(MLT^{-2}\)
(B) \(MT^{-2}\)
(C) \(MT^{-1}\)
(D) \(ML^{-1}T^{-2}\)
✅ Correct: (D)
Q21
The graph between displacement and time for SHM is (Exam: NEET Year: 2019)
(A) straight line
(B) parabola
(C) sine curve
(D) hyperbola
✅ Correct: (C)
Q22
The restoring force in SHM is conservative because (Exam: IIT-JEE Year: 2001)
(A) it depends on velocity
(B) it depends on displacement
(C) work done is path dependent
(D) energy is not conserved
✅ Correct: (B)
Q23
For small oscillations, the motion of a simple pendulum is SHM because (Exam: NEET Year: 2014)
(A) angle is large
(B) \(\sin\theta \approx \theta\)
(C) string is heavy
(D) air resistance is present
✅ Correct: (B)
Q24
The maximum acceleration in SHM is (Exam: JEE Advanced Year: 2017)
(A) \(A\omega\)
(B) \(A\omega^2\)
(C) \(\omega/A\)
(D) \(A^2\omega\)
✅ Correct: (B)
Q25
If the amplitude of SHM is doubled, the total energy becomes (Exam: BITSAT Year: 2016)
(A) double
(B) half
(C) four times
(D) unchanged
✅ Correct: (C)
Q26
The time period of SHM is minimum when (Exam: Olympiad Year: 2013)
(A) mass is maximum
(B) force constant is maximum
(C) amplitude is maximum
(D) displacement is maximum
✅ Correct: (B)
Q27
In SHM, velocity is zero at (Exam: NEET Year: 2020)
(A) mean position
(B) extreme positions
(C) both mean and extreme
(D) everywhere
✅ Correct: (B)
Q28
The phase difference between acceleration and displacement in SHM is (Exam: IIT-JEE Year: 1999)
(A) \(0\)
(B) \(\pi/2\)
(C) \(\pi\)
(D) \(3\pi/2\)
✅ Correct: (C)
Q29
The time period of a pendulum on the Moon is (Exam: NEET Year: 2012)
(A) same as on Earth
(B) less than on Earth
(C) more than on Earth
(D) zero
✅ Correct: (C)
Q30
The displacement in SHM is minimum at (Exam: CBSE Year: 2010)
(A) mean position
(B) extreme positions
(C) midway
(D) everywhere
✅ Correct: (A)
Q31
The velocity-time graph of SHM is (Exam: JEE Main Year: 2015)
(A) linear
(B) parabolic
(C) sinusoidal
(D) circular
✅ Correct: (C)
Q32
The restoring force constant of a spring is doubled. The new time period becomes (Exam: BITSAT Year: 2017)
(A) \(T\)
(B) \(2T\)
(C) \(T/\sqrt{2}\)
(D) \(\sqrt{2}T\)
✅ Correct: (C)
Q33
In SHM, the average kinetic energy over a cycle equals (Exam: KVPY Year: 2014)
(A) zero
(B) total energy
(C) half of total energy
(D) twice the total energy
✅ Correct: (C)
Q34
The condition for SHM is (Exam: IIT-JEE Year: 2003)
(A) force proportional to velocity
(B) force proportional to displacement
(C) force independent of displacement
(D) force proportional to time
✅ Correct: (B)
Q35
The frequency of SHM is (Exam: NEET Year: 2011)
(A) inverse of period
(B) equal to period
(C) square of period
(D) twice the period
✅ Correct: (A)
Q36
The kinetic energy of SHM is maximum when (Exam: JEE Advanced Year: 2018)
(A) displacement is zero
(B) displacement is maximum
(C) acceleration is maximum
(D) force is maximum
✅ Correct: (A)
Q37
A body executes SHM with angular frequency \(\omega\). Its frequency is (Exam: CBSE Year: 2012)
(A) \(\omega\)
(B) \(\omega/2\pi\)
(C) \(2\pi\omega\)
(D) \(\omega^2\)
✅ Correct: (B)
Q38
The motion is SHM if acceleration is (Exam: NEET Year: 2015)
(A) constant
(B) proportional to velocity
(C) proportional to displacement
(D) proportional to square of displacement
✅ Correct: (C)
Q39
The time period of SHM depends on (Exam: IIT-JEE Year: 2000)
(A) amplitude
(B) initial phase
(C) system parameters
(D) displacement
✅ Correct: (C)
Q40
In SHM, the restoring force is zero at (Exam: NEET Year: 2013)
(A) extreme position
(B) mean position
(C) midway
(D) everywhere
✅ Correct: (B)
Q41
The total energy of SHM is proportional to (Exam: BITSAT Year: 2018)
(A) amplitude
(B) square of amplitude
(C) frequency
(D) time period
✅ Correct: (B)
Q42
The acceleration in SHM is maximum at (Exam: CBSE Year: 2014)
(A) mean position
(B) extreme positions
(C) midway
(D) everywhere
✅ Correct: (B)
Q43
A pendulum clock runs slow on a hill because (Exam: NEET Year: 2010)
(A) mass increases
(B) gravity decreases
(C) length increases
(D) air density decreases
✅ Correct: (B)
Q44
The equation of SHM is (Exam: IIT-JEE Year: 1997)
(A) \(x = A\sin(\omega t)\)
(B) \(x = vt\)
(C) \(x = at^2\)
(D) \(x = kt\)
✅ Correct: (A)
Q45
The restoring force constant has SI unit (Exam: CBSE Year: 2015)
(A) N
(B) N/m
(C) J
(D) kg
✅ Correct: (B)
Q46
The motion of a particle is SHM if (Exam: JEE Main Year: 2017)
(A) velocity is constant
(B) force is constant
(C) acceleration is proportional to displacement
(D) displacement is constant
✅ Correct: (C)
Q47
The energy of SHM is equally divided between kinetic and potential energy at (Exam: KVPY Year: 2016)
(A) extreme position
(B) mean position
(C) midway between mean and extreme
(D) everywhere
✅ Correct: (C)
Q48
The time period of SHM increases if (Exam: NEET Year: 2021)
(A) mass increases
(B) force constant increases
(C) amplitude increases
(D) displacement increases
✅ Correct: (A)
Q49
In SHM, the direction of acceleration is always (Exam: IIT-JEE Year: 2005)
(A) along velocity
(B) along displacement
(C) opposite to displacement
(D) perpendicular to velocity
✅ Correct: (C)
Q50
The maximum potential energy of SHM is (Exam: JEE Advanced Year: 2019)
(A) zero
(B) equal to total energy
(C) half of total energy
(D) twice the total energy
✅ Correct: (B)
Frequently Asked Questions
Oscillatory motion is the motion in which a body moves repeatedly to and fro about a fixed mean position under the action of a restoring force.
Periodic motion is a type of motion that repeats itself after equal intervals of time, called the time period.
All oscillatory motions are periodic, but not all periodic motions are oscillatory because oscillatory motion must occur about a mean position.
SHM is a special type of oscillatory motion in which the restoring force is directly proportional to the displacement from the mean position and acts towards it.
A motion is SHM if the restoring force or acceleration is proportional to displacement and opposite in direction, i.e., \(a \propto -x\).
The mean position is the equilibrium position about which a body oscillates and where the net force acting on it is zero.
Amplitude is the maximum displacement of the oscillating body from its mean position.
Time period is the time taken by a body to complete one full oscillation.
Frequency is the number of oscillations completed per second and is the reciprocal of the time period.
Angular frequency \(\omega\) is defined as \(\omega = 2\pi f\), where \(f\) is the frequency of oscillation.
Phase represents the state of oscillation of a particle at a given instant, determined by the argument of the sine or cosine function.
Phase difference is the difference in phase angles of two oscillatory motions at the same instant.
The general equation of SHM is \(x = A\cos(\omega t + \phi)\), where \(A\) is amplitude and \(\phi\) is phase constant.
Restoring force is the force that always acts towards the mean position and tends to bring the body back to equilibrium.
SHM is called harmonic because its displacement varies sinusoidally with time.
