A 0.25-kg mass is oscillating on a spring over a horizontal frictionless surface.When it is at a displacement of 2.8 cm for equilibrium it has a kinetic energy of 1.4 J and a spring potential energy of 2.3 J.What is the maximum speed of the mass during its oscillation?

A) 3.8 m/s
B) 0.2 m/s
C) 5.4 m/s
D) 4.7 m/s
E) 3.4 m/s

Question

A 0.25-kg mass is oscillating on a spring over a horizontal frictionless surface.When it is at a displacement of 2.8 cm for equilibrium it has a kinetic energy of 1.4 J and a spring potential energy of 2.3 J.What is the maximum speed of the mass during its oscillation?
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A) 3.8 m/s
B) 0.2 m/s
C) 5.4 m/s
D) 4.7 m/s
E) ​3.4 m/s

Quizplus · Accepted Answer

We can use the conservation of mechanical energy to solve for the maximum speed of the mass during its oscillation.

At the equilibrium position, the system has a total mechanical energy of:

E = KE + PE
E = 1.4 J + 2.3 J
E = 3.7 J

At the maximum displacement, all the energy is in the form of kinetic energy, so:

E = KE_max
KE_max = 3.7 J

We can now solve for the speed using the formula for kinetic energy:

KE = 0.5mv^2

Plugging in the values, we get:

3.7 J = 0.5(0.25 kg)v^2
v^2 = 29.6
v = 5.4 m/s

Therefore, the maximum speed of the mass during its oscillation is 5.4 m/s, which is answer choice C.

A 025-Kg Mass Is Oscillating on a Spring Over a Horizontal