A small block of mass m on a horizontal frictionless surface is attached to a horizontal spring that has force constant k. The block is pushed against the spring, compressing the spring a distance d. The block is released, and it moves back and forth on the end of the spring. During its motion, what is the maximum speed of the block?

Explanation:

The maximum speed of the block occurs when spring has no deformation, that is, there is no elastic potential energy, which can be remarked from appropriate application of the Principle of Energy Conservation:

People have probably always observed objects in motion and have madeobjects move around. For many centuries, scientists thought they kneweverything about this. However, the Italian scientist Galileo Galilei, wholived  from  1564  to  1642,  began  to  think  about  motion  in  a  new  way.Isaac Newton, who was born the year Galileo died, built upon his dis-coveries and developed three laws. Newton’s laws were revolutionary, asthey seemed to go against everyday experience and observation. Today,parts of Newton's three laws are still the basis for understanding motion.Newton’s First Law: The Law of InertiaNewton’s first law, also known as the Law of Inertia, can be difficult tofully  understand.  It  describes  an  object’s resistance  to  changing  itsmotion and its tendency to keep doing whatever it is doing. A changein motion can be a change in an object’s speed, direction, or both. Forexample, a car that speeds up to pass another car, or that turns a cor-ner is changing its motion. Newton’s first law states that an object’smotion  cannot  change  unless  a  force  acts  on  the  object.  In  otherwords, it takes a force to overcome an object’s inertia and to make theobject go faster, slower, or change direction.