A block is attached to one end of a spring with the other end of the spring fixed to a wall. The block is vibrating horizontally on a frictionless surface. If the mass of the block is 4.0 kg, the spring constant is k

Complete Question

A block is attached to one end of a spring with the other end of the spring fixed to a wall. The block is vibrating horizontally on a frictionless surface. If the mass of the block is 4.0 kg, the spring constant is k = 100 N/m, and the maximum distance of the block from the equilibrium position is 20 cm, what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position?

The velocity is

Explanation:

From the question we are told that

  The mass of the block is  m =  4.0 kg

  The spring constant is k =  100 N/m

  The maximum distance of the block from equilibrium position is  d = 20 cm =0.20 m

   The distance considered is  

Generally the maximum energy stored in the spring is mathematically represented as

=>  

=>  

Gnerally according to the law of energy conservation

   The energy maximum energy of  the spring = energy of  the spring at + energy of the block at

Here energy of the block at is mathematically represented as

=>    

=>    

Generally the energy of the spring at is mathematically represented as

=>    

=>    

So

=>