Frequency is only based on the period of the oscillation; all the other given information is useless for this problem.  Using , we can calculate that the frequency is 0.25 Hz.

The formula for the period of oscillation is

.

When we double the mass, we get:

Because the new factor of 2 is under the square root sign, and also in the numerator, the new period will be increased by .

When the mass is at point , it hasn't traveled at all. When it reaches the spring's equilibrium point, it has traveled a distance of . The mass then continues to a point that's equal to the initial distance traveled, but on the opposite side of the equilibrium point, so the total distance traveled so far is . The mass must then travel back to the starting point to complete the oscillation, so the total distance traveled is .

The formula for determining kinetic energy is 

So, kinetic energy will be greatest when the mass is moving most quickly. The force of the spring on the mass increases the mass's velocity until the spring’s equilibrium point, where the force of the spring acts against the motion of the mass, slowing it down. The mass is moving fastest at the spring's equilibrium point, so that's where its kinetic energy is greatest.

The total energy of the system is 

but due to the face that the mass currently has no velocity, the kinetic energy term goes to zero.

Plugging in the given values, we can solve for the total energy of the system:

Relevant equations:

Write expressions for the initial kinetic and potential energies, if the spring is initially stretched to the maximum amplitude before being released.

Write expressions for the final kinetic and potential energies when the spring crosses the equilibrium point.

Use conservation of energy to equate the initial and final energy sums.

Solve the equation to isolate .

The units for angular frequency, , are radians per second.

We need to derive the equation for angular frequency using conservation of energy.

Rearrange to solve for the velocity:

The velocity is also the product of angular frequency and the distance of the oscillation:

Use this equation to derive the equation for angular frequency:

Finally, use our given mass and spring constant to solve:

At the equilibrium position, the spring does not contribute any potential energy. It is neither stretched, nor compressed.

All of the energy in the system is kinetic energy, resulting from the given velocity:

To solve this question, we will need to use conservation of energy. With no displacement, the ball has a velocity of  and zero displacement. At its maximum displacement, the velocity will be zero and all the energy will be converted to spring potential energy.

Use our given values to solve:

When a mass is in free fall, its potential energy  is increasing. In this instance, all of that energy must be counteracted by the bungee cord, which we can treat like a spring , for the person to come to a stop. This means that we can set these two equations as equal to one another:

We can then rearrange this equation to solve for , the mass at which the bungee cord can be stretched as far as the ground:

Substituting in the known values, we can solve for :