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NCERT Solutions › Physics › Chapter 14

Chapter 14: Oscillations

NCERT Solutions for CBSE Class 10 Physics — 105 solved questions with detailed explanations.

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Questions
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Solved Questions

Q1. In SHM, the acceleration is:

Difficulty: Easy · Topic: SHM Properties

Solution

a = -ω²x. At extreme position x is maximum, so acceleration is maximum.

Q2. The time period of a simple pendulum of length 1 m is approximately (g = π² m/s²):

Difficulty: Easy-Medium · Topic: Simple Pendulum

Solution

T = 2π√(L/g) = 2π√(1/π²) = 2π/π = 2 s.

Q3. The total energy of a particle in SHM is proportional to:

Difficulty: Easy-Medium · Topic: Energy in SHM

Solution

E = ½mω²A². Total energy ∝ A².

Q4. The time period of a simple pendulum of length 25 cm is (g=9.8 m/s²):

Difficulty: Easy-Medium · Topic: Simple Pendulum

Solution

T = 2π√(L/g) = 2π√(0.25/9.8) = 1.0 s.

Q5. The time period of a simple pendulum of length 50 cm is (g=9.8 m/s²):

Difficulty: Easy-Medium · Topic: Simple Pendulum

Solution

T = 2π√(L/g) = 2π√(0.5/9.8) = 1.42 s.

Q6. The time period of a simple pendulum of length 100 cm is (g=9.8 m/s²):

Difficulty: Easy-Medium · Topic: Simple Pendulum

Solution

T = 2π√(L/g) = 2π√(1.0/9.8) = 2.01 s.

Q7. The time period of a simple pendulum of length 200 cm is (g=9.8 m/s²):

Difficulty: Easy-Medium · Topic: Simple Pendulum

Solution

T = 2π√(L/g) = 2π√(2.0/9.8) = 2.84 s.

Q8. The time period of a simple pendulum of length 400 cm is (g=9.8 m/s²):

Difficulty: Easy-Medium · Topic: Simple Pendulum

Solution

T = 2π√(L/g) = 2π√(4.0/9.8) = 4.01 s.

Q9. A mass of 100 g attached to a spring (k=100 N/m) oscillates with period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k) = 2π√(0.1/100) = 0.199 s.

Q10. A mass of 200 g attached to a spring (k=200 N/m) oscillates with period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k) = 2π√(0.2/200) = 0.199 s.

Q11. A mass of 400 g attached to a spring (k=100 N/m) oscillates with period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k) = 2π√(0.4/100) = 0.397 s.

Q12. A mass of 50 g attached to a spring (k=50 N/m) oscillates with period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k) = 2π√(0.05/50) = 0.199 s.

Q13. A mass of 500 g attached to a spring (k=500 N/m) oscillates with period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k) = 2π√(0.5/500) = 0.199 s.

Q14. In SHM, velocity is maximum at:

Difficulty: Easy-Medium · Topic: SHM Properties

Solution

mean position.

Q15. In SHM, acceleration is maximum at:

Difficulty: Easy-Medium · Topic: SHM Properties

Solution

extreme position.

Q16. The phase difference between displacement and velocity in SHM is:

Difficulty: Easy-Medium · Topic: SHM Properties

Solution

π/2 (90°).

Q17. The phase difference between displacement and acceleration in SHM is:

Difficulty: Easy-Medium · Topic: SHM Properties

Solution

π (180°).

Q18. In SHM, KE + PE equals:

Difficulty: Easy-Medium · Topic: SHM Properties

Solution

constant (total energy).

Q19. A spring (k=50 N/m) with mass 0.10 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q20. A spring (k=75 N/m) with mass 0.15 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q21. A spring (k=100 N/m) with mass 0.20 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q22. A spring (k=125 N/m) with mass 0.25 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q23. A spring (k=150 N/m) with mass 0.30 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q24. A spring (k=175 N/m) with mass 0.35 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q25. A spring (k=200 N/m) with mass 0.40 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q26. A spring (k=225 N/m) with mass 0.45 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q27. A spring (k=250 N/m) with mass 0.50 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q28. A spring (k=275 N/m) with mass 0.55 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q29. A spring (k=300 N/m) with mass 0.60 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q30. A spring (k=325 N/m) with mass 0.65 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q31. A spring (k=350 N/m) with mass 0.70 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q32. A spring (k=375 N/m) with mass 0.75 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q33. A spring (k=400 N/m) with mass 0.80 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q34. A spring (k=425 N/m) with mass 0.85 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q35. A spring (k=450 N/m) with mass 0.90 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q36. A spring (k=475 N/m) with mass 0.95 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q37. A spring (k=500 N/m) with mass 1.00 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q38. A spring (k=525 N/m) with mass 1.05 kg has period:

Difficulty: Easy-Medium · Topic: Spring-Mass

Solution

T = 2π√(m/k).

Q39. Pendulum L=10cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=0.635 s.

Q40. Pendulum L=20cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=0.898 s.

Q41. Pendulum L=30cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.099 s.

Q42. Pendulum L=40cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.269 s.

Q43. Pendulum L=50cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.419 s.

Q44. Pendulum L=60cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.555 s.

Q45. Pendulum L=70cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.679 s.

Q46. Pendulum L=80cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.795 s.

Q47. Pendulum L=90cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=1.904 s.

Q48. Pendulum L=100cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.007 s.

Q49. Pendulum L=110cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.105 s.

Q50. Pendulum L=120cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.199 s.

Q51. Pendulum L=130cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.288 s.

Q52. Pendulum L=140cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.375 s.

Q53. Pendulum L=150cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.458 s.

Q54. Pendulum L=160cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.539 s.

Q55. Pendulum L=170cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.617 s.

Q56. Pendulum L=180cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.693 s.

Q57. Pendulum L=190cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.767 s.

Q58. Pendulum L=200cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.838 s.

Q59. Pendulum L=210cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.909 s.

Q60. Pendulum L=220cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=2.977 s.

Q61. Pendulum L=230cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.044 s.

Q62. Pendulum L=240cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.109 s.

Q63. Pendulum L=250cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.173 s.

Q64. Pendulum L=260cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.236 s.

Q65. Pendulum L=270cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.298 s.

Q66. Pendulum L=280cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.359 s.

Q67. Pendulum L=290cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.418 s.

Q68. Pendulum L=300cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.476 s.

Q69. Pendulum L=310cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.534 s.

Q70. Pendulum L=320cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.59 s.

Q71. Pendulum L=330cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.646 s.

Q72. Pendulum L=340cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.701 s.

Q73. Pendulum L=350cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.755 s.

Q74. Pendulum L=360cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.808 s.

Q75. Pendulum L=370cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.861 s.

Q76. Pendulum L=380cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.913 s.

Q77. Pendulum L=390cm. Period (g=9.8):

Difficulty: Easy-Medium · Topic: Pendulum

Solution

T=2π√(L/g)=3.964 s.

Q78. Spring k=10N/m, m=50g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.4443 s.

Q79. Spring k=20N/m, m=50g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.3142 s.

Q80. Spring k=50N/m, m=50g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1987 s.

Q81. Spring k=100N/m, m=50g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1405 s.

Q82. Spring k=200N/m, m=50g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.0993 s.

Q83. Spring k=500N/m, m=50g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.0628 s.

Q84. Spring k=10N/m, m=100g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.6283 s.

Q85. Spring k=20N/m, m=100g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.4443 s.

Q86. Spring k=50N/m, m=100g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.281 s.

Q87. Spring k=100N/m, m=100g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1987 s.

Q88. Spring k=200N/m, m=100g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1405 s.

Q89. Spring k=500N/m, m=100g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.0889 s.

Q90. Spring k=10N/m, m=150g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.7695 s.

Q91. Spring k=20N/m, m=150g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.5441 s.

Q92. Spring k=50N/m, m=150g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.3441 s.

Q93. Spring k=100N/m, m=150g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.2433 s.

Q94. Spring k=200N/m, m=150g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1721 s.

Q95. Spring k=500N/m, m=150g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1088 s.

Q96. Spring k=10N/m, m=200g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.8886 s.

Q97. Spring k=20N/m, m=200g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.6283 s.

Q98. Spring k=50N/m, m=200g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.3974 s.

Q99. Spring k=100N/m, m=200g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.281 s.

Q100. Spring k=200N/m, m=200g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1987 s.

Q101. Spring k=500N/m, m=200g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.1257 s.

Q102. Spring k=10N/m, m=250g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.9935 s.

Q103. Spring k=20N/m, m=250g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.7025 s.

Q104. Spring k=50N/m, m=250g. Period:

Difficulty: Easy-Medium · Topic: Spring

Solution

T=2π√(m/k)=0.4443 s.

Q105. A particle executing SHM has maximum velocity v₀ and maximum acceleration a₀. The time period is:

Difficulty: Medium · Topic: SHM Parameters

Solution

v_max = Aω, a_max = Aω². So ω = a₀/v₀. T = 2π/ω = 2πv₀/a₀.

Other Chapters in Physics

Ch 1: Physical WorldCh 2: Units & MeasurementsCh 3: Motion in a Straight LineCh 4: Motion in a PlaneCh 5: Laws of MotionCh 6: Work Energy & PowerCh 7: System of ParticlesCh 8: GravitationCh 9: Mechanical Properties of SolidsCh 10: Mechanical Properties of FluidsCh 11: Thermal Properties of MatterCh 12: ThermodynamicsCh 13: Kinetic TheoryCh 15: Waves

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