An astronaut visits a moon of Saturn, and decides to measure the accel. of gravity. He ties a rock (m=2 kg) to a rope (1.25 m), pulls the rock back 10 degrees, and releases it into simple harmonic motion. What is the accel due to gravity on the moon? I have no idea where to even start on this problem :(

There was a plotted graph that shows the top of the arc is 10 degrees, and the bottom is -10 deg. and there are two waves in 10 seconds..

To determine the acceleration due to gravity on the moon of Saturn, we can use the information provided about the simple harmonic motion of the rock.

First, let's understand the concept of simple harmonic motion. It is a type of oscillating motion where the object (in this case, the rock) moves back and forth along a path. The motion is periodic and can be described by a sine or cosine function.

In this scenario, the rock is pulled back and released, resulting in oscillatory motion. The angle at the top of the arc is given as 10 degrees, and the bottom is -10 degrees. This means that the amplitude of the oscillation is 10 degrees.

Additionally, it is mentioned that there are two waves in 10 seconds. This information gives us the period of the motion. Since a wave refers to a complete oscillation, two waves in 10 seconds means that the time period (T) is 10/2 = 5 seconds.

Now, to calculate the acceleration due to gravity (g) on the moon, we can use the formula for the period of oscillation (T) in simple harmonic motion:

T = 2π√(m/k)

Where:
T = Time period of oscillation
m = Mass of the object (2 kg)
k = Spring constant (related to the force constant)

In our case, we can replace the spring constant with the acceleration due to gravity (g). Therefore, the equation becomes:

T = 2π√(m/g)

Rearranging the equation, we get:

g = (4π^2 * m) / T^2

Now, substituting the given values:
m = 2 kg
T = 5 seconds

g = (4π² * 2) / 5²

Calculating this expression will give us the acceleration due to gravity on the moon of Saturn.