Answer to Question #160905 in Classical Mechanics for Terry

Question

A block-spring system vibrating on a frictionless, horizontal surface with amplitude of 6.0cm has an energy of 12J. If the block is replaced by one whose mass is twice the mass of the original block and the amplitude of the motion is again 6.0cm, what is the energy of the system?

Answer 1

The total energy of the block-spring system can be found as follows:

$$E=\dfrac{1}{2}kA^2,$$

here, $k$ is the spring constant, $A=6\ cm$ is the amplitude of the motion.

As we can see from the formula, since the spring constant and the amplitude of the motion remains unchanged, the total energy of the block-spring system also remains unchanged.