Lesson 3 - Periodic Motion with SHM - Copy.pptx

General Physics 1_Periodic Motion

1. Periodic Motion

2. What do you notice about the movement?

3. Relate amplitude, frequency, angular frequency, period, displacement, velocity, and acceleration of oscillating systems. STEM_GP12PM-IIc-24 Recognize the necessary conditions for an object to undergo simple harmonic motion. STEM _GP12PM-IIc-25 Calculate the period and frequency of spring-mass systems, simple pendulums, and physical pendulums. STEM_GP12PM-IIc-27 Differentiate underdamped, overdamped, and critically damped motion. STEM_GP12PM-IId-28 Define mechanical wave, longitudinal wave, transverse wave, periodic wave, and sinusoidal wave. STEM_GP12PM-Ild-31 Learning Competencies

4. Session 1 - Introduction to Simple Harmonic Motion Session 2 - Types of Waves Session 3 - Calculating Period and Frequency

5. Introduction to Simple Harmonic Motion Session 1

6. Learning Targets I can describe the characteristics and necessary conditions for simple harmonic motion. I can explain the roles of amplitude, frequency, and period in simple harmonic motion.

7. What is Periodic Motion? It is the motion of an object that returns to its original position at fixed time interval (called period). Example: Swinging pendulum Vibrating molecules Electromagnetic waves (light)

8. Examples of Periodic Motion Simple Harmonic Motion (mass on a spring) Circular Motion (Ferris Wheel) Wave Motion (Sound Wave)

9. Simple Harmonic Motion It can be observed in systems where the displacement of the object is proportional to the force exerted on the object, but this force is directed to the opposite direction Example: Spring-block system

10. Simple Harmonic Motion The block suspended to a spring will move up and down as shown above, this is an example of a simple harmonic motion.

11. There are necessary conditions that must be observed in order for a simple harmonic motion to occur. Conditions for Simple Harmonic Motion No Energy Loss Small Oscillations Restoring Force Mass Equilibrium Position

12.  A force that pushes or pulls the object back to its equilibrium position The restoring force is always directed opposite to the displacement It's proportional to the displacement from equilibrium Mathematically expressed as F = -kx (Hooke's Law) Where F is force, k is spring constant, x is displacement Condition 1: Restoring Force A portrait of Robert Hooke. source: https://brewminate.com/robert-hooke-17th-century-scientist-extraordinaire/

13. F = −kx  is the mathematical representation of Hooke's Law The negative sign indicates the force is opposite to displacement 'k' is the spring constant, measuring the stiffness of the system As displacement increases, the restoring force increases proportionally Hooke’s Law

14. The amplitude of oscillation must be relatively small. This ensures the restoring force remains proportional to displacement Large amplitudes can introduce non-linear effects. Small oscillations maintain the simple harmonic nature of the motion. Condition 2: Small Oscillations

15. Ideally, there should be no friction or air resistance . In reality, some energy loss is inevitable . For SHM, we assume energy conservation within the system. This allows the motion to continue indefinitely without damping . Condition 3: No Energy Loss

16.  The object undergoing SHM must have mass . Mass provides inertia , which is crucial for oscillatory motion. The period of oscillation depends on the mass of the object. Heavier objects generally oscillate more slowly than lighter ones. Condition 4: Mass

17. There must be a well-defined equilibrium position . This is the position where the net force on the object is zero . The object oscillates about this equilibrium position. Displacement is measured from this point. Condition 5: Equilibrium Position

18. There are necessary conditions that must be observed in order for a simple harmonic motion to occur. No Energy Loss Small Oscillations Restoring Force Mass Equilibrium Position Let’s Summarize! Presence of a restoring force proportional to displacement Small oscillations to maintain linearity Negligible energy loss (ideally) Presence of mass Well-defined equilibrium position

19. Simulation Link Activity 6 - Experiment Simple Harmonic Motion

20. How does changing the mass affect the period of oscillation? Explain your reasoning. Let’s Process Effect of mass on the period of oscillation and amplitude Increasing the mass increases the period. The amplitude remains unaffected because there is no damping is present. T

21.   According to the formula for the period of a mass-spring system, where T is the period, m is the mass, and k is the spring constant. The period depends on the square root of the mass, so a larger mass results in a longer period. It takes more time for the system to complete one oscillation.

22. What is the relationship between the spring constant and the period of the oscillation? Let’s Process Effect of spring constant on the period of oscillation The period decreases with a higher spring constant. The amplitude remains unchanged unless damping is present, where stiffer springs may resist amplitude loss more effectively. k  

23.   From the same formula, as the spring constant k increases, the period decreases. A stiffer spring (higher k ) results in faster oscillations because it provides a stronger restoring force.

24. Describe how damping affected the amplitude of the oscillations. Let’s Process Effect of damping on the oscillation Damping reduces the amplitude over time, causing oscillations to gradually diminish until they stop. Higher damping leads to faster amplitude reduction.

25. Damped motion: Oscillatory movement that gradually decreases in amplitude Caused by resistive forces (e.g., friction, air resistance) Three types of damped motion: underdamped : oscillations that decrease in amplitude over time. overdamped : system returns to equilibrium without oscillating critically damped : system returns to equilibrium in the shortest time without oscillating Damping in Oscillation

26. How does energy conservation apply to the system during SHM with and without damping? Let’s Process Energy Conservation in Simple Harmonic Motion Without damping, energy is conserved, and the amplitude remains constant. With damping, energy dissipates, causing the amplitude to decrease until the motion ceases.

27. What did you learn about simple harmonic motion’s characteristics, specifically mass, spring constant, and damping? Let’s Process Conclusion Mass and Period: Larger masses in simple harmonic motion (SHM) lead to slower oscillations due to inertia. Spring Constant and Oscillation Speed: Higher spring constants result in faster oscillations in SHM. Damping and Amplitude: Damping in SHM reduces the amplitude of oscillations over time, eventually bringing the system to rest.

28. Types of Wave Session 2

29. Learning Targets I can define mechanical wave, longitudinal wave, transverse wave, periodic wave, and sinusoidal wave.

30. Mechanical Waves These are disturbances that propagate through a medium, transferring energy without transferring matter. Require a medium to travel (unlike electromagnetic waves) Examples: Sound waves, water waves, seismic waves

31. Mechanical Waves Amplitude: Maximum displacement from equilibrium Wavelength: Distance between two consecutive crests or troughs Frequency: Number of waves passing a point per second.

32. There are necessary conditions that must be observed in order for a simple harmonic motion to occur. Transverse Types of Mechanical Waves Presence of a restoring force proportional to displacement Small oscillations to maintain linearity Negligible energy loss (ideally) Longitudinal Surface

33. These are waves in which particles of the medium vibrate parallel to the direction of wave propagation Characteristics: Compressions (high-pressure regions) and rarefactions (low-pressure regions) No crests or troughs Examples: Sound waves in air, sonar, medical ultrasound Longitudinal Waves

34. These are waves in which particles of the medium vibrate perpendicular to the direction of wave propagation Characteristics: Crests (high points) and troughs (low points). Easily visible wave shape. Examples: Waves on a string Light waves (electromagnetic, not mechanical) Transverse Waves

35. These are waves that repeat their pattern at regular intervals. The waves on the surface of the water are neither longitudinal nor transverse. Characteristics: Constant frequency and wavelength Can have various shapes (e.g., square, triangular) Examples: Ocean waves, sound waves from a tuning fork Surface Waves

36. Mechanical waves are crucial in various fields: Physics: Understanding energy transfer and wave phenomena Engineering: Designing structures to withstand vibrations Geology: Studying seismic waves for earthquake prediction Medicine: Using ultrasound for imaging Applications and Importance

37. Calculating Period and Frequency Session 3

38. Learning Targets I can calculate the period and the frequency of spring-mass, simple pendulum, and physical pendulum

39. Calculating Period and Frequency

40. Spring-Mass System Period: Frequency: where: m = mass of the object (kg) k = spring constant (N/m)  

41. Simple Pendulum Period: Frequency: where: L = length of the pendulum (m) g = acceleration due to gravity (9.8 m/s²)  

42. Physical Pendulum Period: Frequency: where: I = moment of inertia about the pivot point (kg·m²) m = mass of the pendulum (kg) g = acceleration due to gravity (9.8 m/s²) d = distance from pivot to center of mass (m)