Two ideal mass-spring systems, X and Y

PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

Two ideal mass-spring systems, X and Y, oscillate on identical frictionless surfaces. The masses are the same, but the amplitudes differ:

A_X=0.040\,\text{m}

and

A_Y=0.060\,\text{m}

. At every instant, the total mechanical energy of system X is one-half that of system Y. Which of the following is the best estimate of the ratio

k_X/k_Y

of their spring constants? (a)

0.75

(b)

2.3

(c)

1.1

(d)

0.89