What happens if you give the mass a small push?

You might be wondering, how I know to state the initial velocity was to the left, or even why I chose the left side to have the maximum displacement. Try it again, but do so with everything modeled to the right of the starting position. You will find that the answers are the same, because without friction, spring systems have the same properties to either side of equilibrium.

A block of mass m is attached to the end of a spring (spring stiffness constant k). The mass is given an initial displacement x0 from equilibrium, and an initial speed v0. Ignoring friction and the mass of the spring, use energy methods to find (a) its maximum speed, and (b) its maximum stretch from equilibrium, in terms of the given quantities.

Here are other problems these methods could help with:

A mass m is attached to a spring which is held stretched a distance x by a force F, Fig. 6–45, and then released. The spring pulls the mass to the left, towards its natural equilibrium length. Assuming there is no friction, determine the speed of the mass m when the spring returns: (a) to its normal length (x = 0); (b) to half its original extension (x/2).

A vertical spring (ignore its mass), whose spring constant is 875 N􏰀m, is attached to a table and is compressed down by 0.160 m. (a) What upward speed can it give to a 0.380-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

A spring has a spring constant k of 88.0 N/m. How much must this spring be compressed to store 45.0 J of potential energy?

свернуть