# Spring Energy Question

A block of mass M on a horizontal frictionless table is connected to a spring (constant k). The block is at the left and attached to an horizontal spring , and the right end of the spring is itself attached to the wall. The block is set in motion so that it oscillates about its equilibrium point with a certain amplitude Ao. The period of motion is To=2*pi*sqrt(M/k)

A lump of sticky putty of mass m is dropped onto the block. The putty sticks without bouncing. The putty hits M at the instant when M has its maximum velocity. Find:

(1) The new period

(2) The new amplitude

(3) The change in the mechanical energy of the system

https://brainmass.com/physics/energy/spring-energy-question-26154

#### Solution Preview

When all the energy of spring is converted to kinetic energy...

(1/2)k(Ao)^2 = (1/2)Mv^2

You can solve this for v

v = Ao*sqrt(k/M)

This will be the largest velocity.

Now then we drop a piece of putty on the block and the putty sticks. Immediately that tells me to use conservation of momentum and NOT conservation of energy.

so I will call (v1) the ...

#### Solution Summary

When all the energy of spring is converted to kinetic energy, we can use the formula (1/2)k(Ao)^2 = (1/2)Mv^2 to solve for the largest velocity: v = Ao*sqrt(k/M).