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As you know, a common example of a harmonic oscillator is a mass attached to a...

As you know, a common example of a harmonic oscillator is a mass attached to a spring. In this problem, we will consider a horizontally moving block attached to a spring. Note that, since the gravitational potential energy is not changing in this case, it can be excluded from the calculations.

For such a system, the potential energy is stored in the spring and is given by

U=12kx2,

where k is the force constant of the spring and x is the distance from the equilibrium position.

The kinetic energy of the system is, as always,

K=12mv2,

where m is the mass of the block and v is the speed of the block.

We will also assume that there are no resistive forces; that is, E=constant.

A) Find the total energy of the object at any point in its motion.

B) Find the amplitude of the motion.

C) Find the maximum speed attained by the object during its motion.

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