List - I List - II (P) Linear combination of two S.H.M.'s (1) Path of particle will be circular (Q) y = A 1 sin ( ω 1 t ) + A 2 sin ( ω 2 t + ϕ ) (2) S.H.M. for equal frequencies and ampl

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List - I List - II (P) Linear combination of two S.H.M.'s (1) Path of particle will be circular (Q) y = A 1 ​ sin ( ω 1 ​ t ) + A 2 ​ sin ( ω 2 ​ t + ϕ ) (2) S.H.M. for equal frequencies and amplitude (R) x = A sin ω 1 ​ t , y = A sin ω 2 ​ t (3) Superposition may not be a S.H.M. always (S) x = A sin ω t , y = A cos ω t (4) Amplitude will be 2 ​ A for A 1 ​ = A 2 ​ = A , ω 1 ​ = ω 2 ​ and a phase difference of π /2 (5) Path of particle will be straight line for ω 1 ​ = ω 2 ​

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(P) Superposing two S.H.M.s of different frequencies does not give an S.H.M. in general - 3.

(Q) For $A_{1} = A_{2} = A, ω_{1} = ω_{2}, ϕ = π /2$ : $y = A sin ω t + A cos ω t = 2 A sin (ω t + π /4)$ - amplitude $2 A$ - 4.

(R) When $ω_{1} = ω_{2}$ , $y = x$ - straight-line path - 5.

(S) $x^{2} + y^{2} = A^{2}$ - circular path - 1. Hence option (A).

List - I	List - II
(P) Linear combination of two S.H.M.'s	(1) Path of particle will be circular
(Q) $y = A_{1} sin (ω_{1} t) + A_{2} sin (ω_{2} t + ϕ)$	(2) S.H.M. for equal frequencies and amplitude
(R) $x = A sin ω_{1} t$ , $y = A sin ω_{2} t$	(3) Superposition may not be a S.H.M. always
(S) $x = A sin ω t$ , $y = A cos ω t$	(4) Amplitude will be $2 A$ for $A_{1} = A_{2} = A, ω_{1} = ω_{2}$ and a phase difference of $π /2$
	(5) Path of particle will be straight line for $ω_{1} = ω_{2}$

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