**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

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Description: **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 c

Hooke's law states that the restoring force applied by a spring is proportional to the displacement of the spring and opposite in direction. The energy of a particle in SHM changes periodically from P.E to K.E. Both potential and kinetic energy depends upon the square of the displacement.(1) From Hooke's law- ⇒F=kx⇒mg=kx⇒k=mgx⇒k=0.255 kg×9.8 m/s20.475 m⇒k=5.26 N/m (2) Time period of oscillation is given by-T=2πmk ⇒T=2π0.255 kg5.26 N/m⇒T=1.38 s (3) For displacement of 35.6 cm- Potential energy is given as-U=12kx2=12×5.26×(0.356)2 =0.334 J Since 35.6 cm is the maximum stretch from the equilibrium position, i.e., 47.5cm, so at 35.6cm all of the energy is in the form of potential energy. Kinetic energy is zero at this point.⇒Velocity at 35.6cm = 0 m/s So, total energy of the spring-mass system is 0.334 J. For displacement of 26.1cm- Potential energy is given as-U'=12kx'2=12×5.26×(0.261)2 =0.180 J Since total energy of the system is constant and is equal to 0.334 J Therefore, Kinetic energy at 26.1cm is given by-Total energy(T)=Kinetic energy (K')+potential energy (U')⇒K'=T-U'⇒K'=0.334 J-0.180 J⇒K'=0.154 J Now,∵K'=12mv'2⇒v'=2K'm⇒v'=2×0.154 0.255 kg⇒v'=1.10 m/s Conclusion: (1) Spring constant is 5.26 N/m(2) Time period of oscillation is 1.38 s(3) At 35.6cm velocity is zero and potential energy is 0.334 J At 26.1cm velocity is 1.10 m/s and potential energy is 0.180 J

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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.

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.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

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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**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

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