The force of gravity on the blade is , which is the same as 

This unit relationship comes from Newton's second law.

 is the mathematical expression of Newton's second law. The units for force must be a product of the units for mass and the units for acceleration.

Solve the expression by plugging in known values.

The tension in the rope is the sum of the forces acting on it. If one considers that the net force on an object must equal the mass of the object times the acceleration of the object, the net force on the object must be the force due to tension from the rope minus the force due to gravity.

Rearrange the equation. 

Plug in known values.

Since this is a graph of velocity and not position, the curves intersect where the velocities match. Since we do not know the starting position, we do not know where the objects are relative to one another.

Since this is a graph of velocity vs. time, its integral is distance travelled. We can estimate the integral by looking at the area under the curves. Since Bbject 1 has a greater area under its velocity curve, it has covered a greater distance. Its velocity is greater that Object 2's for the entire time, so it makes sense that it will travel farther.

The y velocity is the time derivative of the  position, and not the  derivative. In order to find it, use the chain rule:

Of course, 

From the force diagram above, we can see that tension  is pulling up on both sides of the string and gravity is pulling down on both blocks. With this information we can write 2 force equations:

If we add the two equations together, we get:

where 

Solving for , we get 

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.