Question

A 1-kg object is attached to a spring of force constant k = 0.5 kN/m. The spring is stretched 10 cm from equilibrium and released. What is the kinetic energy of the mass–spring system when the mass is 5.0 cm from its equilibrium position? Group of answer choices

2.95 J

2.32 J

3.48 J

2.71 J

1.88 J

Answer 1

Given mass-spring system is a simple harmonic oscillator.

Spring constant , k= 0.5 kN/m=500 N/m

Maximum displacement of the mass is

At maximum displacement, the velocity of the mass is zero

Energy of the system at maximum displacement is

Energy of the system when the displacement is x = 5 cm =0.05 m

Where K is the Kinetic energy of the system at x=5 cm as the mass will have some speed at this position.

By Law of Conservation of energy,

Kinetic energy of the system is