Question

The ratio of force constants of two springs is 1:5. The equal mass suspended at the free ends of both springs are performing S.H.M. If the maximum acceleration for both springs are equal, the ratio of amplitudes for both springs is …….. 

(A) (1/√5) 

(B) (1/5) 

(C) (5/1) 

(D) (√5/1)

Answer 1

The correct option (C) (5/1)

Explanation:

a_max = A ∙ ω²

ω² = {(a_max) /A} (1)

also

ω = √(k/m)

i.e.

ω² = (k/m)   (2)

from (1) & (2)

(k/m) = {(a_max)/A}

A = a_max ∙ (m/k)

both masses are equal ∴ m same a_max is both for both springs

i.e. A = {(constant)/K}

∴ AK = constant

A ∝ (1/K)

∴ (A₁/A₂) = (K₂/K₁) = (5/1)