time period of linear shm questions with solutions

Showing 1–10 of 43 questions

• NumericmediumSimple Harmonic Motiontime period of linear shm

  A uniform U-tube contains a liquid column of total length 5 m and is placed in an elevator accelerating upward at 2.5 m/s². Take g = 10 m/s². If ω² = N s⁻², find N.

  Your answer

  Check answerShow answer

  JEE MainsNEETJEE Advanced

  Open question & full solution →
• MCQmediumSimple Harmonic Motiontime period of linear shm

  A block of mass m is attached to an ideal horizontal spring of force constant k inside a vehicle accelerating uniformly with acceleration a along the spring. Relative to the vehicle, what happens to the equilibrium position and the small-oscillation time period?

  Options

  • Option A

    Both remain unchanged.

  • Option B

    Equilibrium shifts by ma/k, but T remains 2π√(m/k).

  • Option C

    T becomes 2π√[m/(k+ma)].

  • Option D

    SHM is impossible in the accelerating frame.

  Check answerShow answer

  JEE MainsNEETJEE Advanced

  Open question & full solution →
• MCQmediumSimple Harmonic Motiontime period of linear shm

  For a block of mass m attached to a spring k along the smooth face of a freely moving wedge of mass M and angle θ, which pair gives the equilibrium extension xₑ and the angular frequency ω of small oscillations relative to the wedge?

  Options

  • Option A

    xₑ = mg sinθ/k, ω² = k(M+m)/[m(M+m sin²θ)]

  • Option B

    xₑ = Mmg sinθ/[k(M+m)], ω² = k/m

  • Option C

    xₑ = mg cosθ/k, ω² = k(M+m)/(mM)

  • Option D

    xₑ = 2mg sinθ/k, ω² = k/(M+m)

  Check answerShow answer
  Open question & full solution →
• NumericmediumSimple Harmonic Motiontime period of linear shm

  The time period of simple harmonic motion of mass M in the given figure is π√(αM/5K), where the value of α is _______.

  

  Your answer

  Check answerShow answer

  JEE Mains 2024 31 Jan Evening Shift

  Open question & full solution →
• IntegereasySimple Harmonic Motiontime period of linear shm

  A particle executes simple harmonic motion along the x-axis and satisfies v² = 50-x², where x is displacement and v is speed in consistent SI units. If the time period of the motion is X / 7 seconds, find X to the nearest integer.

  Your answer

  Check answerShow answer

  JEE Mains 2026 4 April Morning Shift

  Open question & full solution →
• Multi-correctmediumSimple Harmonic Motiontime period of linear shm

  A block attached to a horizontal ideal spring is observed from a frame accelerating uniformly along the spring direction. Which statements are correct?

  Select all that apply

  • Option A

    A constant pseudo-force shifts the equilibrium position.

  • Option B

    The shift magnitude is ma/k when the frame acceleration magnitude is a.

  • Option C

    The angular frequency about the new equilibrium remains √(k/m).

  • Option D

    A constant frame acceleration does not by itself change the spring force constant.

  Check answerShow answer

  JEE MainsNEETJEE Advanced

  Open question & full solution →
• MCQmediumSimple Harmonic Motiontime period of linear shm

  Two blocks of masses m and M (M > m) are placed one over the other on a frictionless horizontal table. The lower block M is attached to a spring of constant k, and the coefficient of friction between the blocks is μ. The system is slightly displaced and released. Consider: (A) T = 2π√[(M+m)/k]; (B) a = -kx/(M+m); (C) the friction magnitude on the upper block is mμ|x|/(M+m); (D) maximum amplitude without slipping is μ(M+m)g/k; (E) maximum frictional force can be μ(M+m)g. Choose the correct set.

  

  Options

  • Option A

    C, D, E only

  • Option B

    A, B, C only

  • Option C

    A, B, D only

  • Option D

    B, C, D only

  Check answerShow answer

  JEE Mains 2025 3 April Morning Shift

  Open question & full solution →
• Multi-correctmediumSimple Harmonic Motiontime period of linear shm

  Which statements are correct for ideal spring-mass oscillators?

  Select all that apply

  • Option A

    Two springs attached to opposite sides of a block contribute additively to the restoring constant.

  • Option B

    For springs in series, reciprocal spring constants add.

  • Option C

    A uniform spring of mass mₛ fixed at one end contributes an effective mass mₛ/3 in the standard fundamental-mode approximation.

  • Option D

    The time period of a vertical spring-mass oscillator about equilibrium is independent of g.

  Check answerShow answer

  JEE MainsNEETJEE Advanced

  Open question & full solution →
• MCQmediumSimple Harmonic Motiontime period of linear shm

  A cube of side 10 cm and mass 10 g oscillates vertically in water of density 10³ kg/m³. Take g=10 m/s². Find its time period.

  Options

  • Option A

    π/25 s

  • Option B

    π/50 s

  • Option C

    π/100 s

  • Option D

    2π/25 s

  Check answerShow answer

  JEE Mains 2025 23 Jan Morning Shift

  Open question & full solution →
• MCQeasySimple Harmonic Motiontime period of linear shm

  A mass m is suspended from a uniform spring and oscillates with frequency ν₁. The same spring is cut into two equal halves, and the same mass is suspended from one half. If the new frequency is ν₂, what is ν₂ /ν₁?

  Options

  • Option A

    1

  • Option B

    2

  • Option C

    √2

  • Option D

    √3

  Check answerShow answer

  JEE Mains 2026 8 April Evening Shift

  Open question & full solution →