A 0.20-kg mass is oscillating on a spring over a horizontal frictionless surface.When it is at a displacement of 2.6 cm for equilibrium it has a kinetic energy of 1.4 J and a spring potential energy of 2.2 J.What is the maximum speed of the mass during its oscillation?
A)3.7 m/s
B)4.7 m/s
C)6.0 m/s
D)6.3 m/s

Question

Quizplus · Accepted Answer

The total mechanical energy of the mass-spring system is the sum of the kinetic and potential energies:

E = K + U = 1.4 J + 2.2 J = 3.6 J

At the maximum displacement (amplitude) of the oscillation, all of the energy is in the form of kinetic energy, since the spring is momentarily at rest.

Thus,

E = K_max = (1/2)mv_max^2

Solving for v_max, we get

v_max = sqrt((2E)/m) = sqrt((2*3.6 J)/(0.20 kg))

v_max ≈ 6.0 m/s

A 020-Kg Mass Is Oscillating on a Spring Over a Horizontal