Two identical masses perform separate horizontal oscillations on frictionless surfaces

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

Problem

Two identical masses perform separate horizontal oscillations on frictionless surfaces, each attached to a different spring. For mass

m

the two springs have force constants

k_1 = 100\,\text{N}\,\text{m}^{-1}

and

k_2 = 250\,\text{N}\,\text{m}^{-1}

respectively. In both cases the amplitude of oscillation is

0.10\,\text{m}

. (i) Calculate the ratio of the maximum speeds

v_{\text{max},1} : v_{\text{max},2}

. (ii) Calculate the ratio of the maximum accelerations

a_{\text{max},1} : a_{\text{max},2}

. (iii) Which oscillator possesses the greater maximum kinetic energy and by what factor? Show complete working.