Oscillations

29 NEET-UG practice questions on Oscillations, part of Physics. The first 25 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Easy
A block on a vertical spring oscillates with period T on Earth. If the same system is taken to the Moon, where gravity is g/6, what is its period?
1. AT
2. BT/√6
3. C√6 T
4. D6T
Show answerHide answer
Answer: A · T
T = 2π√(m/k) contains neither g nor anything that depends on it. Gravity only shifts the equilibrium position. So the period stays T.
- B: This inverts even the pendulum dependence on g.
- C: This applies the simple pendulum formula to the spring.
- D: This treats the period as inversely proportional to g.
Remember this
A spring's period is independent of g; a simple pendulum's period varies as 1/√g.
Question 2 · Hard
A block on a smooth horizontal surface oscillates on a spring with an amplitude of 8 cm. As it passes through the mean position, a lump of clay of equal mass is dropped gently on it and sticks. What is the new amplitude?
1. A4 cm
2. B8√2 cm
3. C4√2 cm
4. D8 cm
Show answerHide answer
Answer: C · 4√2 cm
Momentum conservation halves the speed at the mean position: v' = v/2. Mass doubling gives ω' = ω/√2, so A' = v'/ω' = (v/2)(√2/ω) = A/√2 = 4√2 cm. Check by energy: the kinetic energy becomes (1/2)(2m)(v/2)² = half the old value, so A² halves.
- A: This halves the speed but keeps ω unchanged.
- B: This scales the amplitude up by √2 instead of down.
- D: This is the result if the clay lands at an extreme position.
Remember this
Added mass at the mean position reduces the amplitude; added mass at an extreme leaves it unchanged.
Question 3 · Medium
The displacement of a particle is x = 0.05 sin(20t + π/3), in SI units. Find its speed when x = 0.03 m.
1. A0.8 m/s
2. B1.0 m/s
3. C0.4 m/s
4. D0.6 m/s
Show answerHide answer
Answer: A · 0.8 m/s
v = ω√(A² − x²) = 20√(0.0025 − 0.0009) = 20 × 0.04 = 0.8 m/s. Check by energy: v² + (ωx)² = 0.64 + 0.36 = 1.0 = (Aω)². The initial phase does not matter.
- B: This is the maximum speed, Aω.
- C: This uses ω(A − x) instead of ω√(A² − x²).
- D: This uses ωx instead of ω√(A² − x²).
Remember this
The speed at position x is ω√(A² − x²), and the initial phase plays no part.
Question 4 · Medium
Consider a particle in simple harmonic motion of amplitude A. A. Its total mechanical energy stays constant in time. B. Its kinetic energy is greatest at the mean position. C. Its kinetic and potential energies are equal at x = A/2. D. The magnitude of its acceleration is greatest at the extreme positions. Which statements are correct?
1. AB, C and D only
2. BA, C and D only
3. CA, B and D only
4. DA and B only
Show answerHide answer
Answer: C · A, B and D only
Total energy (1/2)kA² is constant, kinetic energy peaks at x = 0, and |a| = ω²|x| peaks at x = A, so A, B and D hold. Kinetic and potential energies are equal when (1/2)kx² = (1/4)kA², at x = A/√2, so C is false.
- A: This includes the false C and misses A.
- B: This includes the false C and misses B.
- D: This misses D, which follows from a = −ω²x.
Remember this
KE equals PE at x = A/√2, not at A/2; at x = A/2, KE = 3 PE.
Question 5 · Easy
By what phase does the acceleration of a particle in simple harmonic motion differ from its displacement?
1. AZero
2. Bπ
3. Cπ/2
4. Dπ/4
Show answerHide answer
Answer: B · π
Acceleration a = −ω²x is always directed opposite to the displacement, so the two differ in phase by π.
- A: This ignores the minus sign in a = −ω²x.
- C: π/2 is the phase difference between velocity and displacement.
- D: No standard pair in SHM has this phase difference.
Remember this
Velocity leads displacement by π/2; acceleration leads displacement by π.
Question 6 · Medium
A simple pendulum experiment gives a straight-line graph of T² against length L, with a slope of 4 s²/m. Taking π² = 10, what value of g does this give?
1. A0.4 m/s²
2. B40 m/s²
3. C10 m/s²
4. D2.5 m/s²
Answer and explanation in LearnFree account
Question 7 · Hard
Using the displacement-time graph drawn, choose the equation of this simple harmonic motion, with x in cm and t in s.
Figure: MedExams
1. Ax = 4 sin(πt/12 + π/6)
2. Bx = 4 sin(πt/6 + π/6)
3. Cx = 4 cos(πt/6 + π/6)
4. Dx = 4 sin(πt/6 + 5π/6)
Answer and explanation in LearnFree account
Question 8 · Easy
Displacement of a particle in SHM is plotted against time. What are its amplitude and frequency?
Figure: MedExams
1. A4 cm and 0.8 Hz
2. B8 cm and 1.25 Hz
3. C4 cm and 2.5 Hz
4. D4 cm and 1.25 Hz
Answer and explanation in LearnFree account
Question 9 · Medium
Acceleration a and displacement x of a particle in simple harmonic motion, of amplitude A, are related as in which graph?
Figure: MedExams
1. AGraph B
2. BGraph D
3. CGraph C
4. DGraph A
Answer and explanation in LearnFree account
Question 10 · Medium
A 1 kg block on a spring oscillates about x = 0, and its potential energy is plotted against x. What is its speed as it passes x = 0.1 m?
Figure: MedExams
1. A√3 m/s
2. B1 m/s
3. C2 m/s
4. D√2 m/s
Answer and explanation in LearnFree account
Question 11 · Easy
Match List-I with List-II for a particle of mass m in simple harmonic motion x = A sin ωt. List-I (Quantity) A. Maximum speed B. Maximum acceleration C. Total mechanical energy D. Time period List-II (Expression) I. 2π/ω II. Aω² III. Aω IV. (1/2)mω²A² Choose the correct answer from the options given below.
1. AA-II, B-III, C-IV, D-I
2. BA-III, B-II, C-I, D-IV
3. CA-III, B-II, C-IV, D-I
4. DA-III, B-IV, C-II, D-I
Answer and explanation in LearnFree account
Question 12 · Medium
For a simple pendulum swinging with small amplitude at a given place, the time period is independent of
1. AThe acceleration due to gravity
2. BThe mass of the bob
3. CThe length of the string
4. DThe latitude of the place
Answer and explanation in LearnFree account
Question 13 · Medium
Two identical springs, each of force constant 200 N/m, are joined end to end. A 1 kg mass hung from this combination is set into vertical oscillation. What is its period?
1. A0.14π s
2. B0.1π s
3. C0.2π s
4. D0.02π s
Answer and explanation in LearnFree account
Question 14 · Hard
A particle performs simple harmonic motion x = A sin(2πt/T). What is the shortest time it takes to go from x = +A/2 to x = −(√3/2)A?
1. AT/6
2. B7T/12
3. CT/4
4. DT/12
Answer and explanation in LearnFree account
Question 15 · Medium
During simple harmonic motion of amplitude A, at what displacement from the mean position is the kinetic energy three times the potential energy?
1. AA/2
2. BA/3
3. CA/√2
4. D(√3/2)A
Answer and explanation in LearnFree account
Question 16 · Easy
For a particle in simple harmonic motion, which is true at the mean position?
1. ABoth speed and acceleration are maximum
2. BBoth speed and acceleration are zero
3. CSpeed is maximum and acceleration is zero
4. DSpeed is zero and acceleration is maximum
Answer and explanation in LearnFree account
Question 17 · Medium
A block of mass m on a spring of force constant k oscillates with period T. The spring is replaced by two identical springs, each of force constant k, attached side by side (in parallel) to the same block. What is the new period?
1. A√2 T
2. BT/√2
3. CT/2
4. D2T
Answer and explanation in LearnFree account
Question 18 · Hard
A particle in simple harmonic motion has a speed of 8 cm/s when it is 3 cm from the mean position and 6 cm/s when it is 4 cm from it. What are its amplitude and period?
1. A5 cm and π s
2. B25 cm and π s
3. C7 cm and π s
4. D5 cm and π/2 s
Answer and explanation in LearnFree account
Question 19 · Medium
The displacement of a particle is x = 0.05 sin(10t), with x in metres and t in seconds. What is the maximum acceleration of the particle?
1. A500 m/s²
2. B5 m/s²
3. C0.05 m/s²
4. D0.5 m/s²
Answer and explanation in LearnFree account
Question 20 · Medium
Match List-I with List-II. List-I (Oscillating system) A. Simple pendulum of length l at a place where gravity is g B. Block of mass m on a spring of force constant k C. Block of mass m on two springs, each of force constant k, joined in series D. Simple pendulum of length l in a lift accelerating upward at a List-II (Period) I. 2π√(m/k) II. 2π√(l/g) III. 2π√(l/(g + a)) IV. 2π√(2m/k) Choose the correct answer from the options given below.
1. AA-II, B-I, C-IV, D-III
2. BA-II, B-IV, C-I, D-III
3. CA-III, B-I, C-IV, D-II
4. DA-II, B-I, C-III, D-IV
Answer and explanation in LearnFree account
Question 21 · Medium
On a smooth floor, a block of mass 0.5 kg fixed to a spring of force constant 200 N/m oscillates with an amplitude of 10 cm. What is its speed at the instant its potential energy equals its kinetic energy?
1. A1 m/s
2. B√2 m/s
3. C√3 m/s
4. D2 m/s
Answer and explanation in LearnFree account
Question 22 · Easy
The amplitude of a spring-block oscillator is doubled, the block and spring being unchanged. By what factor does its total mechanical energy change?
1. AIt becomes √2 times
2. BIt becomes four times
3. CIt doubles
4. DIt stays the same
Answer and explanation in LearnFree account
Question 23 · Medium
For a particle in simple harmonic motion, consider the following statements: A. A graph of its velocity against its displacement is an ellipse. B. A graph of its acceleration against its displacement is a straight line through the origin with a negative slope. C. A graph of its kinetic energy against its displacement is a parabola with its maximum at the mean position. D. Its potential energy varies with time with the same period as its displacement. Which of these are correct?
1. AB and C only
2. BA, B and D only
3. CA, C and D only
4. DA, B and C only
Answer and explanation in LearnFree account
Question 24 · Medium
Two particles oscillate along the same line with x₁ = A sin(ωt + π/6) and x₂ = A cos ωt. What is the phase difference between them?
1. Aπ/2
2. B2π/3
3. Cπ/6
4. Dπ/3
Answer and explanation in LearnFree account
Question 25 · Hard
A particle moves according to x = (4 cm) sin(πt/6), with t in seconds. What total distance does it cover between t = 0 and t = 4 s?
1. A(8 − 2√3) cm
2. B4 cm
3. C2√3 cm
4. D(4 + 2√3) cm
Answer and explanation in LearnFree account

4 more Oscillations questions

Answer them one by one, keep your score and see your weak topics in Learn. Signed-out visitors try 25 per exam; sign in with Google to see them all.

Study Physics

Oscillations

A block on a vertical spring oscillates with period T on Earth. If the same system is taken to the Moon, where gravity is g/6, what is its period?

A block on a smooth horizontal surface oscillates on a spring with an amplitude of 8 cm. As it passes through the mean position, a lump of clay of equal mass is dropped gently on it and sticks. What is the new amplitude?

The displacement of a particle is x = 0.05 sin(20t + π/3), in SI units. Find its speed when x = 0.03 m.

By what phase does the acceleration of a particle in simple harmonic motion differ from its displacement?

A simple pendulum experiment gives a straight-line graph of T² against length L, with a slope of 4 s²/m. Taking π² = 10, what value of g does this give?

Using the displacement-time graph drawn, choose the equation of this simple harmonic motion, with x in cm and t in s.

Displacement of a particle in SHM is plotted against time. What are its amplitude and frequency?

Acceleration a and displacement x of a particle in simple harmonic motion, of amplitude A, are related as in which graph?

A 1 kg block on a spring oscillates about x = 0, and its potential energy is plotted against x. What is its speed as it passes x = 0.1 m?

For a simple pendulum swinging with small amplitude at a given place, the time period is independent of

Two identical springs, each of force constant 200 N/m, are joined end to end. A 1 kg mass hung from this combination is set into vertical oscillation. What is its period?

A particle performs simple harmonic motion x = A sin(2πt/T). What is the shortest time it takes to go from x = +A/2 to x = −(√3/2)A?

During simple harmonic motion of amplitude A, at what displacement from the mean position is the kinetic energy three times the potential energy?

For a particle in simple harmonic motion, which is true at the mean position?

A block of mass m on a spring of force constant k oscillates with period T. The spring is replaced by two identical springs, each of force constant k, attached side by side (in parallel) to the same block. What is the new period?

A particle in simple harmonic motion has a speed of 8 cm/s when it is 3 cm from the mean position and 6 cm/s when it is 4 cm from it. What are its amplitude and period?

The displacement of a particle is x = 0.05 sin(10t), with x in metres and t in seconds. What is the maximum acceleration of the particle?

On a smooth floor, a block of mass 0.5 kg fixed to a spring of force constant 200 N/m oscillates with an amplitude of 10 cm. What is its speed at the instant its potential energy equals its kinetic energy?

The amplitude of a spring-block oscillator is doubled, the block and spring being unchanged. By what factor does its total mechanical energy change?

Two particles oscillate along the same line with x₁ = A sin(ωt + π/6) and x₂ = A cos ωt. What is the phase difference between them?

A particle moves according to x = (4 cm) sin(πt/6), with t in seconds. What total distance does it cover between t = 0 and t = 4 s?