Physics 211-Module 4 Hands On Activities Packet Part 2 c. What is the speed of the block when the displacement from equilibrium is 5 cm? Hint: use conservation of mechanical energy. Student Add Name Here d. What is the maximum speed during these oscillations? Hint: use conservation of energy and think about what the potential energy is when the speed is maximum. e. The experiment is repeated with the same mass and spring, but the amplitude is doubled. What happens to each of the following quantities: unchanged doubles
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.
plz just do part c, d e.

![### Simple Harmonic Motion of a Spring-Ball System
#### Problem Statement:
2. **The graph shows the x position of a small ball hooked onto a spring of spring constant 2000 N/m.**
**a. What is the mass of the ball?**
**b. What is the maximum potential energy stored in the spring during the oscillations? Assume U = 0 at equilibrium.**
#### Graph Description:
The graph on the right presents the displacement (x) versus time for the small ball attached to a spring. Key features to note in the graph include:
- **Y-Axis (Displacement x in cm):** This axis represents the position of the ball in centimeters (cm).
- The range extends from 0 cm to 40 cm.
- **X-Axis (Time in ms):** This axis measures time in milliseconds (ms).
- The range extends from 0 ms to 30 ms.
The graph shows the oscillatory motion of the ball with periodic peaks and troughs, indicative of simple harmonic motion.
#### Important Measurements from the Graph:
- **Amplitude (A):** The peak displacement from the equilibrium position.
- From the graph, A ≈ 40 cm.
- **Period (T):** The time taken to complete one full cycle of oscillation.
- From the graph, T ≈ 25 ms (estimated from peak to peak).
#### Solutions:
**a. Determining the Mass of the Ball:**
Given:
- Spring constant \( k = 2000 \) N/m
- Amplitude \( A \approx 40 \) cm \( = 0.4 \) m (converted to meters)
- Period \( T \approx 25 \) ms \( = 0.025 \) s (converted to seconds)
Using the formula for the period of a spring-mass system:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
Rearranging to solve for mass \( m \):
\[ m = \frac{T^2 k}{4\pi^2} \]
Substituting in the known values:
\[ m = \frac{(0.025)^2 \cdot 2000}{4\pi^2} \approx 0.00398 \text{ kg} \]
**b. Maximum Potential Energy:**
The potential energy stored in a spring at maximum displacement (amplitude](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed9646ce-15b0-415b-bd6e-483299f8afd8%2F66acfe92-1e8a-43a8-a708-c525f64d6b00%2Fezfgrxm_processed.jpeg&w=3840&q=75)

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