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Amplitude of a combination of sine and cosine terms (superposed SHMs)

This type of question, asked 5 times: 2021 Paper 13, 2021 Paper 19, 2021 Paper 21, 10 Apr 2023, 2 Apr 2025. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 13

    4
    If a particle is performing SHM such that X=Asin(ωt)+Bcos(ωt)X=Asin(\omega t) +Bcos(\omega t). Then the equation of SHM can also be represented as x=Csin[ωt+ϕ]x=Csin\lbrack\omega t+\phi\rbrack. The C&ϕC\&\phi are

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  2. Question 2

    2021 Paper 19

    26
    Two simple harmonic motions are represented by the equations x1=5sin⁡(2πt+π4)x_{1}= 5\sin\left( 2\pi t +\frac{\pi}{4} \right) and x2=52(sin⁡2πt+cos⁡2πt)x_{2}= 5\sqrt{2}(\sin2\pi t + \cos2\pi t). The amplitude of second motion is ______ times the amplitude in first motion.

  3. Question 3

    2021 Paper 21

    22
    Two simple harmonic motion, are represented by the equations y1=10sin⁡(3πt+π3)y_{1}= 10\sin\left( 3\pi t +\frac{\pi}{3} \right) y2=5(sin⁡3πt+3cos⁡3πt)y_{2}= 5(\sin3\pi t +\sqrt{3}\cos3\pi t) Ratio of amplitude of y1y_{1} to y2=x:1y_{2}=x:1. The value of xx is

  4. Question 4

    10 Apr 2023

    104
    For a periodic motion represented by the equation Y=sin⁡ωt+cos⁡ωtY = \sin\omega t + \cos\omega t The amplitude of the motion is

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  5. Question 5

    2 Apr 2025

    9
    A particle is subjected two simple harmonic motions as : x1=7sin⁡5t cmx_{1}=\sqrt{7}\sin 5t\ cm and x2=27sin⁡(5t+π3)cmx_{2}= 2\sqrt{7}\sin\left( 5t+\frac{\pi}{3} \right)cm where x is displacement and tt is time in seconds. The maximum acceleration of the particle is x×10−2 ms−2x \times10^{- 2}{\text{ }ms}^{- 2}. The value of x is :

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