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Time after starting from the mean position at which kinetic and potential energy are in a given ratio

This type of question, asked 7 times: May 2022 S1, 10 May 2023 S2, 15 May 2023 S1, 12 May 2024 S2, 25 Apr 2025 S2, 15 Apr 2026 S1, 14 May 2026 S2. All 7 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    31
    A particle starts oscillating simple harmonically from its mean position with time period TT. At time t=T12t = \frac{T}{12}, the ratio of the potential energy to kinetic energy of the particle is (sin⁡30°=cos⁡60°=0.5, cos⁡30°=sin⁡60°=32\sin 30° = \cos 60° = 0.5,\ \cos 30° = \sin 60° = \frac{\sqrt{3}}{2})

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  2. Question 2

    10 May 2023 S2

    13
    A particle starts oscillating simple harmonically from its equilibrium position with time period 'T'. What is the ratio of potential energy to kinetic energy of the particle at time t=T12t = \frac{T}{12}? (sin⁡π6=12)\left(\sin\frac{\pi}{6} = \frac{1}{2}\right)

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  3. Question 3

    15 May 2023 S1

    30
    Starting from mean position, a body oscillates simple harmonically with a period TT. After what time will its kinetic energy be 75% of the total energy? sin⁡30∘=0.5\sin 30^{\circ}=0.5

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  4. Question 4

    12 May 2024 S2

    4
    A particle starts from mean position and performs S.H.M. with period 4 second. At what time its kinetic energy is 50% of total energy? (cos⁡45∘=12)\left(\cos 45^\circ = \frac{1}{\sqrt{2}}\right)

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  5. Question 5

    25 Apr 2025 S2

    34
    A particle starts oscillating simple harmonically from its mean position with time period ' TT '. At time t=T6t =\frac{T}{6}, the ratio of the potential energy to kinetic energy of the particle is [sin⁡30∘=cos⁡60∘=0⋅5,cos⁡30∘=sin⁡60∘=3/2]\left\lbrack \sin30^{\circ}= \cos60^{\circ}= 0 \cdot 5,\cos30^{\circ}= \sin60^{\circ}=\sqrt{3}/2 \right\rbrack

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  6. Question 6

    15 Apr 2026 S1

    119
    A particle starts from mean position and performs S.H.M. with period 66 second. At what time its kinetic energy is 50%50\% of total energy? (cos⁡45∘=1/2)(\cos 45^\circ = 1/\sqrt{2})

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  7. Question 7

    14 May 2026 S2

    118
    A particle starts oscillating simple harmonically from its equilibrium position with time period T. The ratio of kinetic energy to potential energy of the particle at time t=T/12t = T/12 is

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