Two light, ideal springs are connected in series between a rigid ceiling support and…

PHYSICS · Multi-part · CBSE · Physics · Oscillations · Oscillations

Problem

Two light, ideal springs are connected in series between a rigid ceiling support and a

0.500\,\text{kg}

block, as shown in the verbal description below. • Spring 1 (closest to the ceiling) has a known force constant of

150\,\text{N}\!\cdot\!\text{m}^{-1}

. • Spring 2 (attached to the block) has an unknown force constant

k_{2}

. • The combined system is set into small vertical oscillations. The average time for 20 complete oscillations is measured to be

34.0\,\text{s}

. Air resistance is negligible, and the springs are assumed massless. (a) Derive an expression for the effective force constant

k_{\text{eq}}

of two ideal springs connected in series. (b) Using the measured period, determine the numerical value of

k_{\text{eq}}

for the series combination. (c) Calculate the force constant

k_{2}

of Spring 2. (d) Briefly discuss whether the numerical value of

k_{2}

would be more sensitive to uncertainty in the measured period or to uncertainty in the stated value of Spring 1’s constant, and justify your answer qualitatively.

Related theory

Browse the problem library