Two light springs A and B have force constants and respectively

PHYSICS · Subjective · CBSE · Physics · Oscillations · Oscillations

Problem

Two light springs A and B have force constants

k

and

2k

respectively. Their upper ends are fixed to a rigid support, while their lower ends are tied together to carry a single mass

m

so that the springs act in parallel. (i) Obtain an expression for the effective force constant

k_{\text{eff}}

of the combination. (ii) Derive an expression for the natural angular frequency of vertical oscillation of the mass in terms of

k

and

m

. (iii) If

k = 120\,\text{N}\,\text{m}^{-1}

and

m = 0.50\,\text{kg}

, calculate the natural frequency of the system.