### Determining Free-Fall Acceleration on a New Planet Using a Pendulum**Problem Statement:**You land on a new planet and would like to figure out its freefall acceleration, \( g_p \). You make a pendulum out of a solid disk as shown below:![Diagram of solid disk pendulum](cosmetic-description)In the diagram:- The solid disk is colored yellow.- The pendulum is pivoted at a point just outside its circumference.- The disk is depicted with its radius \( R \) extending from the center to the edge.- The center of mass (COM) of the disk is indicated by a blue "x," located a distance of \( R/2 \) from the circumference.- A dotted line represents the path the COM will follow as the disk oscillates.- \( \theta_0 \) is the small initial angle of displacement from the vertical.**Given Data:**- Total mass of disk, \( m = 2 \) kg- Radius of disk, \( R = 0.25 \) m- Period of oscillation, \( T = 1.5 \) s**Objective:**To determine the acceleration due to gravity, \( g_p \), on the new planet.**Explanation of the Diagram:**The diagram is a side view of a pendulum made from a solid disk. The pendulum is fixed at a point on the edge of the disk and allowed to oscillate. The initial displacement angle \( \theta_0 \) is very small. The center of mass (COM) of the disk is marked with a blue "x," which is at a distance \( R/2 \) from the pivot point. This distance forms the effective length of the pendulum.**Steps to Determine \( g_p \):**1. **Identify the effective length of the pendulum, \( L \)**: This is the distance from the pivot point to the center of mass of the disk. For a solid disk, this distance is \( R/2 \).2. **Use the formula for the period of a physical pendulum**: \[ T = 2\pi \sqrt{\frac{I}{mgL}} \] Where: - \( I \) is the moment of inertia of the disk about the pivot. - \( m \) is the mass of the disk. - \( g

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Description: ### Determining Free-Fall Acceleration on a New Planet Using a Pendulum**Problem Statement:**You land on a new planet and would like to figure out its freefall acceleration, \( g_p \). You make a pendulum out of a solid disk as shown below:![Diagram

Time period for the compound pendulum is given by the formula T=2πIcm+mL2mgLWhere Icm is the moment…

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6. You land on a new planet and would like to figure out its freefall acceler- ation, gp. You make a pendulum out of a solid disk as seen below: Joo R/2 Suppose the disk has total mass m = 2 kg and radius R = 0.25 m. Its COM is indicated by the blue "x" on the diagram, a distance of R/2 from the circumference. Ensuring that is very small, you let the pendulum oscillate and measure that its total period is T = 1.5 s. What is gp?

6. You land on a new planet and would like to figure out its freefall acceler- ation, gp. You make a pendulum out of a solid disk as seen below: Joo R/2 Suppose the disk has total mass m = 2 kg and radius R = 0.25 m. Its COM is indicated by the blue "x" on the diagram, a distance of R/2 from the circumference. Ensuring that is very small, you let the pendulum oscillate and measure that its total period is T = 1.5 s. What is gp?

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Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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### Determining Free-Fall Acceleration on a New Planet Using a Pendulum

**Problem Statement:**

You land on a new planet and would like to figure out its freefall acceleration, \( g_p \). You make a pendulum out of a solid disk as shown below:

![Diagram of solid disk pendulum](cosmetic-description)

In the diagram:
- The solid disk is colored yellow.
- The pendulum is pivoted at a point just outside its circumference.
- The disk is depicted with its radius \( R \) extending from the center to the edge.
- The center of mass (COM) of the disk is indicated by a blue "x," located a distance of \( R/2 \) from the circumference.
- A dotted line represents the path the COM will follow as the disk oscillates.
- \( \theta_0 \) is the small initial angle of displacement from the vertical.

**Given Data:**
- Total mass of disk, \( m = 2 \) kg
- Radius of disk, \( R = 0.25 \) m
- Period of oscillation, \( T = 1.5 \) s

**Objective:**
To determine the acceleration due to gravity, \( g_p \), on the new planet.

**Explanation of the Diagram:**

The diagram is a side view of a pendulum made from a solid disk. The pendulum is fixed at a point on the edge of the disk and allowed to oscillate. The initial displacement angle \( \theta_0 \) is very small.

The center of mass (COM) of the disk is marked with a blue "x," which is at a distance \( R/2 \) from the pivot point. This distance forms the effective length of the pendulum.

**Steps to Determine \( g_p \):**
1. **Identify the effective length of the pendulum, \( L \)**: This is the distance from the pivot point to the center of mass of the disk. For a solid disk, this distance is \( R/2 \).

2. **Use the formula for the period of a physical pendulum**:
\[
T = 2\pi \sqrt{\frac{I}{mgL}}
\]
Where:
- \( I \) is the moment of inertia of the disk about the pivot.
- \( m \) is the mass of the disk.
- \( g

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