A body of unknown mass is attached to the lower end of a light vertical spring

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A body of unknown mass

m

is attached to the lower end of a light vertical spring. When set into small vertical oscillations the period is measured to be

T_1 = 0.40\,\text{s}

. (i) Deduce, in terms of

m

, the spring constant

k

of the spring. (ii) Another body of mass

0.50\,\text{kg}

is gently placed on the first body so that both masses move together. The new period of small vertical oscillations is found to be

T_2 = 1.5\,T_1

. Show that the unknown mass is approximately

0.40\,\text{kg}

. (iii) Using the value of

m

obtained in part (ii), calculate the numerical value of the spring constant and the natural linear frequency of oscillation before the second body was added.

Related theory

Simple Harmonic Motion (SHM)
Simple harmonic motion
Pendulum and spring systems
Oscillations

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