Since we are told that the block is 1m above its lowest point (half way between its low point and horizontal), we can calculate the angle that the pendulum makes with the vertical:

Then we can use the following expression to determine the net force acting on the block in the direction of its motion:

Then we can use Newton's 2nd law to determine the instantaneous acceleration:

Canceling out mass and rearranging for acceleration:

Since we know the velocity of the block as it travels through the horizontal, we can directly calculate the distance above horizontal that the block reaches using the expression for conservation of energy:

If we assume that horizontal has a height of 0, we can eliminate initial potential energy. We can also eliminate final kinetic energy as the block should be at rest when it reaches its highest point.

Plugging in expressions for each variable, we get:

Eliminating mass and rearranging for final height, we get:

Plugging in our values, we get:

This is the distance the block reaches above the horizontal, so we need to add this to the distance between horizontal and the blocks lowest point, which is simply the length of the pole:

The lowest maximum velocity occurs in the scenario where the block is at rest when the pendulum is vertical and pointing upward. Therefore, even the slightest additional movement will result in the pendulum rotating in complete circles With this in mind, we can begin with the expression for conservation of energy:

If we say the initial condition is when the block is at the lowest point of rotation (when it is traveling at its maximum velocity), and assume that point to have a height of 0, we can eliminate initial potential energy. Furthermore, our final state will then be when the block is at the highest point of rotation and at rest. Thus we can eliminate final kinetic energy to get:

Plugging in expressions for each variable, we get:

Eliminating mass and rearranging for maximum velocity, we get:

Where the maximum height is two times the length of the pendulum:

Since the maximum angle achieved by the pendulum is very small, we can use the follow expression to determine the angle of the pendulum at any time :

Note how we are using the cosine function since the pendulum began at its highest point. We already have all of these values, so we can simply plug and chug:

The block experiences its maximum velocity when it is at its lowest point of rotation and its minimum velocity at its highest point of rotation. Therefore, we can use the expression for conservation of energy to solve this problem:

If we assume that the initial condition is when the block is at the low point of rotation and assume that that point has a height of 0, then we can eliminate initial potential energy:

Now substituting in expressions for each of these:

Eliminating mass and multiplying both sides of the expression by 2, we get:

Then rearranging for final velocity:

Where the height is simply twice the length of the pendulum:

Plugging in our values:

Since we are given the length of the pendulum and told that it begins at rest and in the horizontal position, we can calculate the maximum velocity of the block as it travels through its lowest point using the expression for conservation of energy:

We can eliminate initial kinetic energy since the pendulum begins at rest. We can also eliminate final potential energy if we assume that the height at the lowest point of rotation is equal to 0.

Substituting in expressions for each of these:

Where the initial height is just the length of the pendulum:

Rearranging for final velocity, we get:

We can then calculate centripetal acceleration from this:

Where the radius is the length of the pendulum:

We can begin with the expression for conservation of energy to solve this problem:

The block will achieve its maximum velocity at the lowest point of rotation. If we say that this point has a height of 0, we can eliminate initial potential:

Plugging in expressions for each of these:

Multiplying both sides of the expression by , we get:

Now let's say that the final condition is when the block has a velocity of . Rearranging for the final height, we get:

Plugging in our values:

This is the height that the block is above our reference point when it reaches the desired speed. From here, we can develop an expression for the height of the block as a function of the angle the block makes with the vertical. First, let's begin with a function that tells us how far below the block is from the horizontal:

If this does not make sense, draw it out. d is the distance below the horizontal, L is the length of the pendulum, and theta is the angle between the pendulum and the horizontal.

Moving on, we can take this expression to develop one that tells us the height of the block:

Rearranging for angle:

Now plugging in our values:

We can use the equation for conservation of energy to solve this problem.

If the initial state is when the mass is at its highest position and the final state is when the mass is at its lowest position, then we can eliminate initial kinetic energy and final potential energy:

Substituting expressions in for each term, we get:

Canceling out mass and rearranging for height, we get:

Thinking about a pendulum practically, we can write the height of the mass at any given point as a function of the length and angle of the pendulum:

Think about how this formula is written. The second term gives us how far down the mass is from the top point. Therefore, we need to subtract this from the length of the pendulum to get how high above the lowest point (the height) the mass currently is.

Substituting this into the previous equation, we get:

Rearrange to solve for the angle:

We have values for each variable, allowing us to solve:

To find the answer one must manipulate the equation

Where  represents the period of the motion,  the length of the pendulum, and  the gravity or acceleration the system is under.

To solve this for  we will start by dividing both sides by . Next will with square both sides and finally multiply by , to come to the form below

Now plugging in our numbers

Keep in mind that the most accurate method is to round numbers at the very end of calculations (above this isn't done from the start of pi for simplicity).

The unit calculation above will end with meters as we are taking which will leave  as the final unit of your answer.

To calculate torque, this equation is needed:

Next, identify the given information:

Plug these numbers into the equation to determine the torque: