Angular Simple Harmonic Motion and Its Time Period questions with solutions

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• MCQmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  A pendulum is hung from the roof of a sufficiently high building and moves freely to and fro like a simple harmonic oscillator. The acceleration of the bob is 20 m s⁻² at a distance of 5 m from the mean position. The time period of oscillation is:

  Options

  • Option A

    2 s

  • Option B

    π s

  • Option C

    2π s

  • Option D

    1 s

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• A/RmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  Choose the correct option for the following Assertion (A) and Reason (R).

  Assertion

  A simple pendulum inside a uniformly accelerating vehicle can still execute small SHM about a shifted equilibrium direction.

  Reason

  In the accelerating frame, gravity and the constant pseudo-acceleration combine to produce a constant effective gravity vector.

  Options

  • Option A

    Both A and R are true and R is the correct explanation of A.

  • Option B

    Both A and R are true but R is NOT the correct explanation of A.

  • Option C

    A is true but R is false.

  • Option D

    A is false but R is true.

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• NumericmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  A simple pendulum of length 1 m is inside a vehicle accelerating horizontally at 7.5 m/s². Take g = 10 m/s². If the square of the angular frequency about the new equilibrium is N/4 s⁻², find N.

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• NumericmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  A simple pendulum of length 100 cm and bob mass 250 g executes SHM of amplitude 10 cm. The maximum tension in the string is (x/40) N. The value of x is ______.

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• MCQeasySimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  A body performs angular simple harmonic motion about a fixed axis with angular amplitude θ₀ and time period T. At an instant its angular displacement is +θ₀/2 and it is moving towards the positive angular extreme +θ₀. How much additional time is required to reach the extreme?

  Options

  • Option A

    T/12

  • Option B

    T/8

  • Option C

    T/6

  • Option D

    T/4

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• MCQdifficultSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  A uniform rod OO′ of length l is hinged at O. Two identical massless springs are attached as in Fig. 1: one at l/2 and one at l. In Fig. 2 both springs are attached at l/2. Ignoring gravity and for small angular oscillations, the frequencies are f₁ and f₂. Find f₁/f₂.

  

  Options

  • Option A

    2

  • Option B

    √2

  • Option C

    √(5/2)

  • Option D

    √(2/5)

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• Multi-correctmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  Which statements are correct for angular SHM and physical pendulums under the small-angle approximation?

  Select all that apply

  • Option A

    A physical pendulum satisfies Iθ̈ = -Mgdθ.

  • Option B

    Its time period is 2π√[I/(Mgd)].

  • Option C

    A torsional oscillator satisfies Iθ̈ = -Cθ.

  • Option D

    A torsional oscillator has time period 2π√(I/C).

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• MCQeasySimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  Assertion: At the peak of a mountain, the time period of a pendulum increases. Reason: The time period of a pendulum increases when g decreases.

  Options

  • Option A

    Assertion is correct, Reason is incorrect

  • Option B

    Assertion is incorrect, Reason is correct

  • Option C

    Assertion is incorrect, Reason is incorrect

  • Option D

    Assertion is correct, Reason is correct

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• MCQmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  A simple pendulum of length l is suspended inside a vehicle accelerating horizontally with constant acceleration a. After the bob reaches its new equilibrium direction, it is displaced through a small angle about that direction and released. What is the time period of small oscillations?

  Options

  • Option A

    2π√(l/g)

  • Option B

    2π√[l/√(g²+a²)]

  • Option C

    2π√[l/(g+a)]

  • Option D

    2π√[l/(g-a)]

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• MCQmediumSimple Harmonic MotionAngular Simple Harmonic Motion and Its Time Period

  Two simple pendulums have lengths ℓ₁ and ℓ₂ and undergo small angular displacements θ₁ and θ₂ from their mean positions. If their angular accelerations have equal magnitude at an instant, which relation is correct?

  Options

  • Option A

    θ₁ℓ₁ = θ₂ℓ₂

  • Option B

    θ₁ℓ₁² = θ₂ℓ₂²

  • Option C

    θ₁ℓ₂² = θ₂ℓ₁²

  • Option D

    θ₁ℓ₂ = θ₂ℓ₁

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