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:

We can determine the vertical components by using some geometry.

Since this problem boils down to being a problem of conservation of energy, we can state that

Since the mass is released from rest and we can state at the bottom of its arc it will be at height 0 m, this equation can be simplified:

 is equal to the height of the mass above 0 m; therefore, by referring to the diagram, we can determine that . By plugging this in and rearranging the equation, we can solve for the speed of the mass when the string is vertically aligned:

When the object is released, it has no kinetic energy (it isn't moving) and a potential energy of

When the object passes through the equilibrium point, it has no potential energy () and a kinetic energy of

Due to the conservation of energy, these two quantities must be equal to each other:

First, we should convert 80 centimeters to 0.8 meters.

We know the force applied to the weight by gravity is

The force applied by the spring in the opposite direction must be equal to this:

The angular velocity of the harmonic system is equal to the square root of the spring constant over the mass:

Since we need the angular velocity to be  and we are given the spring constant as , then we can set up an equation:

The velocity equation can be found by differentiating the position equation.

Here, we made use of the chain rule in taking the derivative.

We need to know three things to solve this problem.

1. Formula for frequency of a spring in simple harmonic motion
2. The spring constant
3. Mass of object attached to spring

We're given 2 and 3, so we just need to know 1.

The formula for frequency is:

Plugging in our values, we get:

Now we need to convert Hertz (cycles per second) to cycles per minute.

To get to these units:

We simply need the expression for the period of a pendulum to solve this problem:

Rearranging for length, we get:

We have all of these values, allowing us to solve: