What are some types of repetitive motion?

​Essential Question:

I am learning about the periodic motion of a spring and transverse, longitudinal, and surface mechanical waves.

​Learning Objective:

TEKS: P.8A Periodic Motion

​What is periodic motion?

Definition: Any motion that repeats in a regular cycle.

Examples: Swinging pendulum, vibrating spring, and ocean waves.

​Key Vocabulary:

1. Period: The time required for one complete cycle of motion.

2. Amplitude: The maximum displacement from the equilibrium position.

3. Simple Harmonic Motion: A motion where the restoring force is proportional to displacement.

4. Hooke’s Law: The force acting on a spring is proportional to the stretched amount.

5. Simple Pendulum: A weight suspended from a string that swings back and forth.

6. Resonance: When small forces are applied at regular intervals, increasing the amplitude of vibration.

• ​F= force exerted by the spring (Newtons)

• K= spring constant (N/m)

• X= displacement from equilibrium (mass)

​Hooke's Law

Example Calculation: If a spring has a constant of 5N/m and is stretched by 0.2m, what is the force?

Answer:
F=

​Hooke's Law

Example Calculation: If a spring has a constant of 5N/m and is stretched by 0.2m, what is the force?

Answer:
F=-(5N/m)(.02)= -1N

​Hooke's Law

Simple Pendulums

• T= Period (s)

• L= Length of Pendulum (m)

• G= Gravitational Acceleration 9.8 (m/s)^2 

• Key Idea: Longer pendulums take longer to complete one swing

Mechanical Waves

​Definition: Waves that transfer energy through a medium.

Types:
Transverse Waves: Particles move perpendicular to wave motions (light waves, water waves).
Longitudinal Waves: Particles move parallel to wave motion (sound waves).
Surface Waves: Combination of transverse and longitudinal motion (ocean waves).

Graphs show periodic motion over time.

Key properties:
Amplitude: Height of wave crest

Period: Time between peaks

Frequency: Number of cycles per second

​

​Displacement vs. Time Graph

​Activity: Pendulum Investigation

Materials: String, weights, stopwatch, and ruler
Procedure:
1. Construct a simple pendulum with a string and weight
2. Measure and record the length of the string
3. Pull the pendulum to a small angle and release it
4. Time how long it takes to complete 10 swings
5. Calculate the period (T=total time/10)
6. Repeat this with a longer string and compare the results.

​Constructed Response Prompt

Explain how the length of a pendulum affects its period. Use your data to support your answer.