Oscillations

10 NEET-UG practice questions on Oscillations, part of Physics. The first 10 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

1. 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

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   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.

2. 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

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   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.

3. 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

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   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.

4. 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

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   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.

5. 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

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   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.

6. 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

7. 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.

   

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   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

8. Question 8 · Easy

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

   

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   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

9. Question 9 · Medium

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

   

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   1. AGraph B
   2. BGraph D
   3. CGraph C
   4. DGraph A

   Answer and explanation in LearnFree account

10. 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?

    

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    1. A√3 m/s
    2. B1 m/s
    3. C2 m/s
    4. D√2 m/s

    Answer and explanation in LearnFree account