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physical pendulam and torsional pendulam ,combination of shm questions with solutions
Practice Simple Harmonic Motion for JEE Main, JEE Advanced, NEET, and Classes 11–12. Attempt each question, then open it for the full solution.
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- MCQmediumSimple Harmonic Motion
A particle is subjected to two simple harmonic motions: x₁ = √7 sin(5t) cm and x₂ = 2√7 sin(5t + π/3) cm. The maximum acceleration is x×10⁻² m s⁻². The value of x is:
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JEE Mains 2025 2 April Morning Shift
Open question & full solution → - A/RmediumSimple Harmonic Motion
Choose the correct option for the following Assertion (A) and Reason (R).
Assertion
Two mutually perpendicular SHMs of the same frequency and phase difference π/2 produce an elliptical path in general.
Reason
Eliminating time from x = A cosωt and y = B sinωt gives x²/A² + y²/B² = 1.
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Open question & full solution → - MCQmediumSimple Harmonic Motion
A particle simultaneously executes two mutually perpendicular oscillations given by x = A cosωt and y = B cos2ωt. Which equation represents the trajectory after eliminating time?
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A uniform disc of mass M and radius R can oscillate in its own plane about a fixed horizontal axis passing through a point A on its rim, as shown in the figure. For small angular oscillations under gravity, what is its time period?
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JEE Mains 2026 4 April Evening Shift
Open question & full solution → - NumericmediumSimple Harmonic Motion
A particle executes two perpendicular SHMs given by x = 3cos5t and y = 4sin5t, where x and y are in metres and t is in seconds. If its maximum resultant speed is N m/s, find N.
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A thin ring of radius 0.50 m is suspended from a point on its circumference and oscillates in its own vertical plane. Take g = 10 m/s². If ω² = N s⁻², find N.
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Open question & full solution → - MCQmediumSimple Harmonic Motion
A uniform rod of length L is used as a physical pendulum. Its pivot can be chosen at any point on the rod at distance a from the centre. For small oscillations, at what value of a is the time period minimum?
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Open question & full solution → - NumericeasySimple Harmonic Motion
A body of moment of inertia 2×10⁻³ kg·m² is suspended by a torsion wire of torsional constant 0.18 N·m/rad. If the square of its angular frequency is N s⁻², find N.
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Open question & full solution → - NumericmediumSimple Harmonic Motion
A tank contains two immiscible liquids of densities 6ρ and 2ρ. The higher density liquid is filled up to a height L/2 from the bottom. A thin rod of density ρ and length L is fully immersed and hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly disturbed from its equilibrium, the time period of small oscillations is (2π/n)√(L/g), where g is the acceleration due to gravity. The value of n is:
JEE Advanced2026Paper 1
Open question & full solution → - MCQmediumSimple Harmonic Motion
Two identical uniform rods, each of length L and mass m, are rigidly joined at right angles to form an L-shaped body. The body is pivoted at the free end of one rod and is free to oscillate in its own vertical plane. Which expression gives the angular frequency of small oscillations about the stable equilibrium?
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