Question

As shown in figure, the object having mass M is executing S.H.M. with an amplitude A. The amplitude of point P shown in figure will be…….

(A) {(K₁A)/K₂}

(B) {(K₂A)/K₁}

(C) {(K₁A)/(K₁ + K₂)}

(D) {(K₂A)/(K₁ + K₂)}

Answer 1

The correct option (D) {(K₂A)/(K₁ + K₂)}

Explanation:

Kℓ  = constant

∴ K₁ℓ₁ = K₂ℓ₂ = kℓ 

∴ ℓ₂ = {(K₁ℓ₁)/K₂} also ℓ₁ + ℓ₂ = ℓ = A

K₁ & K₂ are in series hence resultant

K = {(K₁ ∙ K₂)/(K₁ + K₂)}

∴ {(K₁ + K₂)/K₂} = (K₁/K)

As K₁ ℓ₁ = Kℓ

∴ (K₁/K) = (ℓ/ℓ₁)

∴ (ℓ/ℓ₁)  = {(K₁ + K₂)/K₂}

(ℓ₁/ℓ) = {K₂/(K₁ + K₂)} hence ℓ₁ = [K₂/{K₁ + K₂}] A

∴ amplitude at P = {(AK₂)/(K₁ + K₂)}