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Phase difference between two given SHM equations

This type of question, asked 2 times: 9 May 2024 S2, 15 Apr 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    9 May 2024 S2

    50
    Two S.H.M.s are represented by equations y1=0.1sin⁡ ⁣(100πt+π3)y_1 = 0.1\sin\!\left(100\pi t + \frac{\pi}{3}\right) and y2=0.1cos⁡(100πt)y_2 = 0.1\cos(100\pi t). The phase difference between the speeds of the two particles is

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  2. Question 2

    15 Apr 2026 S2

    119
    The minimum phase difference between two simple harmonic motions is x1=12sin⁡ωt+12cos⁡ωtx_1 = \dfrac{1}{\sqrt{2}}\sin\omega t + \dfrac{1}{\sqrt{2}}\cos\omega t x2=sin⁡ωt+cos⁡ωtx_2 = \sin\omega t + \cos\omega t [sin⁡π4=cos⁡π4=12]\left[\sin\dfrac{\pi}{4} = \cos\dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}}\right]

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