A physics lab is demonstrating the principles of simple harmonic motion (SHM) by using a spring affixed to a horizontal support. The student is asked to find the spring constant, k. After suspending a mass of 255.0 g from the spring, the student notices the spring is displaced 47.5 cm from its previous equilibrium. With this information, calculate the spring constant. spring constant: N/m When the spring, with the attached 255.0 g mass, is displaced from its new equilibrium position, it undergoes SHM. Calcula the period of oscillation, T, neglecting the mass of the spring itself.

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**Title: Exploring Simple Harmonic Motion (SHM) with Springs**

In this physics lab activity, students are introduced to the principles of simple harmonic motion (SHM) by experimenting with a spring affixed to a horizontal support. The task involves calculating the spring constant, denoted as \( k \).

**Experiment Procedure:**

1. A mass of 255.0 g is suspended from the spring.
2. This suspension causes the spring to displace by 47.5 cm from its original equilibrium position.

**Objective 1: Calculate the Spring Constant**

Using the provided displacement information, students will determine the spring constant (\( k \)).

- **Spring Constant Formula:**

\[
\text{Spring Constant: } \_\_\_ \, \text{N/m}
\]

**Objective 2: Determine the Period of Oscillation**

Once the spring is extended with the mass, it undergoes simple harmonic motion when displaced from its new equilibrium position. Students are tasked with calculating the period of oscillation (\( T \)), ignoring the mass of the spring itself.

- **Period of Oscillation Formula:**

\[
T = \_\_\_ \, \text{s}
\]

Students will use the principles of SHM to complete these calculations, enhancing their understanding of dynamics and spring mechanics.
Transcribed Image Text:**Title: Exploring Simple Harmonic Motion (SHM) with Springs** In this physics lab activity, students are introduced to the principles of simple harmonic motion (SHM) by experimenting with a spring affixed to a horizontal support. The task involves calculating the spring constant, denoted as \( k \). **Experiment Procedure:** 1. A mass of 255.0 g is suspended from the spring. 2. This suspension causes the spring to displace by 47.5 cm from its original equilibrium position. **Objective 1: Calculate the Spring Constant** Using the provided displacement information, students will determine the spring constant (\( k \)). - **Spring Constant Formula:** \[ \text{Spring Constant: } \_\_\_ \, \text{N/m} \] **Objective 2: Determine the Period of Oscillation** Once the spring is extended with the mass, it undergoes simple harmonic motion when displaced from its new equilibrium position. Students are tasked with calculating the period of oscillation (\( T \)), ignoring the mass of the spring itself. - **Period of Oscillation Formula:** \[ T = \_\_\_ \, \text{s} \] Students will use the principles of SHM to complete these calculations, enhancing their understanding of dynamics and spring mechanics.
In the final section of the lab, the student is asked to investigate the energy distribution of the spring system described previously. The student pulls the mass down an additional 35.6 cm from the equilibrium point of 47.5 cm when the mass is stationary and allows the system to oscillate. Using the equilibrium point of 47.5 cm as the zero point for total potential energy, calculate the velocity and total potential energy for each displacement given and insert the correct answer.

| Displacement (cm) from equilibrium | Velocity (m/s) | Total potential energy (J) |
|------------------------------------|----------------|----------------------------|
| 35.6                               |                |                            |
| 26.1                               |                |                            |

**Answer Bank:**

- 1.62
- 0.334
- 1.10
- 0.594
- 0.180
Transcribed Image Text:In the final section of the lab, the student is asked to investigate the energy distribution of the spring system described previously. The student pulls the mass down an additional 35.6 cm from the equilibrium point of 47.5 cm when the mass is stationary and allows the system to oscillate. Using the equilibrium point of 47.5 cm as the zero point for total potential energy, calculate the velocity and total potential energy for each displacement given and insert the correct answer. | Displacement (cm) from equilibrium | Velocity (m/s) | Total potential energy (J) | |------------------------------------|----------------|----------------------------| | 35.6 | | | | 26.1 | | | **Answer Bank:** - 1.62 - 0.334 - 1.10 - 0.594 - 0.180
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