time period of linear shm questions with solutions

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• NumericmediumSimple Harmonic Motiontime period of linear shm

  A mass of 3 kg is attached to two ideal springs of force constants 100 N/m and 300 N/m connected in series on a smooth horizontal surface. If the square of the angular frequency is N s⁻², find N.

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• NumericmediumSimple Harmonic Motiontime period of linear shm

  In the figure, a block of mass M = 490 g placed on a frictionless table is connected with two springs having same spring constant K = 2 N m⁻¹. If the block is displaced horizontally, the number of complete oscillations it will make in 14π s is ______.

  

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• MCQmediumSimple Harmonic Motiontime period of linear shm

  A mass M is suspended from the lower end of a vertical elastic rod of length L, cross-sectional area A and Young's modulus Y. The rod mass is negligible. If the mass is displaced slightly vertically and released, what is the time period of longitudinal oscillation?

  Options

  • Option A

    2π√[ML/(YA)]

  • Option B

    2π√[MAY/L]

  • Option C

    2π√[MY/(AL)]

  • Option D

    2π√[MA/(YL)]

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• NumericmediumSimple Harmonic Motiontime period of linear shm

  A solid sphere of mass 5 kg rolls without slipping while its centre is attached to a spring of force constant 70 N/m. If the square of the angular frequency of small oscillations is N s⁻², find N.

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• MCQmediumSimple Harmonic Motiontime period of linear shm

  Two ideal springs of force constants k₁ and k₂ are connected in series and a mass m is attached to the free end on a smooth horizontal surface. Which expression gives the time period of small oscillations?

  Options

  • Option A

    2π√[m(k₁+k₂)/(k₁k₂)]

  • Option B

    2π√[mk₁k₂/(k₁+k₂)]

  • Option C

    2π√[m/(k₁+k₂)]

  • Option D

    2π√[m(k₁-k₂)/(k₁k₂)]

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• Multi-correctmediumSimple Harmonic Motiontime period of linear shm

  Which statements are correct for ideal liquid-column oscillations in tubes?

  Select all that apply

  • Option A

    For a U-tube, the restoring head difference is twice the displacement of either free surface.

  • Option B

    For an asymmetric V-tube, ω² = g(sinα+sinβ)/L.

  • Option C

    For an upward-accelerating elevator, g is replaced by g+a in the U-tube formula.

  • Option D

    Viscosity, if significant, would introduce damping and spoil ideal undamped SHM.

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• MCQeasySimple Harmonic Motiontime period of linear shm

  A block of mass m is placed on a smooth horizontal surface and connected between two ideal springs fixed to opposite walls. The left spring has force constant k and the right spring has force constant 2k. If the block is displaced slightly and released, what is its angular frequency?

  Options

  • Option A

    √(k/m)

  • Option B

    √(2k/m)

  • Option C

    √(3k/m)

  • Option D

    √[k/(3m)]

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• MCQmediumSimple Harmonic Motiontime period of linear shm

  A uniform solid disc of mass M and radius R rolls without slipping on a rough horizontal surface. Its centre is connected to a horizontal ideal spring of force constant k. What is the angular frequency of small oscillations?

  Options

  • Option A

    √(k/M)

  • Option B

    √[2k/(3M)]

  • Option C

    √[3k/(2M)]

  • Option D

    √[5k/(7M)]

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• Multi-correctmediumSimple Harmonic Motiontime period of linear shm

  A rigid body rolls without slipping while attached to a spring and executes small oscillations. Which statements are correct under ideal rolling conditions?

  Select all that apply

  • Option A

    Rotational kinetic energy increases the effective inertia of the oscillator.

  • Option B

    For a spring attached to the centre, Mₑ = M+I/R².

  • Option C

    For a material point initially at the top, the spring extension can be approximately 2x for small rolling displacement x.

  • Option D

    A solid sphere with centre spring has ω² = 5k/(7M).

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• MCQmediumSimple Harmonic Motiontime period of linear shm

  A uniform solid sphere of mass M and radius R rolls without slipping. A horizontal spring of force constant k is attached to the material point that is uppermost in the equilibrium position. For sufficiently small oscillations, the spring extension may be taken as twice the displacement x of the centre. What is the angular frequency?

  Options

  • Option A

    √[5k/(7M)]

  • Option B

    √[10k/(7M)]

  • Option C

    √[20k/(7M)]

  • Option D

    2√(k/M)

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