Ablock of mass 2.0 kg sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 800 n/m) which has its other end fixed. if the speed of the block as it passes through the equilibrium position is 4.0 m/s, what is its speed when it is a distance of 10 cm from the equilibrium position?

To solve this problem it is necessary to apply the concepts related to the conservation of Energy. In this case we must apply the conservation of the initial kinetic energy, as well as the final kinetic energy together with the elastic potential energy. Mathematically this can be expressed as,

Where,

m = Mass

= Initial Velocity

= Final Velocity

k = Spring constant

x = Displacement

Our values are given as,

Replacing we will have to,

Solving to find the final velocity we have that,

Therefore the speed when it is a distance of 10cm from the equlibrium position is 3.4641m/s