Demonstrating What Changes the Period of Simple Harmonic Motion(SHM)

Summary

This educational video explains the concept of simple harmonic motion (SHM), focusing on the period of motion for mass-spring systems and pendulums. It discusses the factors affecting the period, including mass, spring constant, and pendulum length. The script emphasizes that amplitude does not impact the period in SHM. For pendulums, it clarifies that if the amplitude exceeds 15 degrees, the motion is no longer simple harmonic. Additionally, the video explores how the mass and spring constant in mass-spring systems, as well as gravity in pendulums, influence their periods. The goal is to provide a thorough understanding of SHM's behavior and the formulas governing it.

Takeaways

• 😀 The period of simple harmonic motion (SHM) is the time it takes to complete one full cycle.
• 😀 The symbol for period is 'T', and its units are typically seconds or seconds per cycle, but could also be minutes, hours, or even days.
• 😀 A full cycle in SHM can be described using positions 1, 2, and 3, with position 1 being the maximum displacement (amplitude) from equilibrium, and position 2 being the equilibrium position.
• 😀 If an object starts at position 1, a full cycle goes through positions 2, 3, 2, and back to 1.
• 😀 Amplitude does not affect the period of simple harmonic motion. Changing the amplitude does not alter the time it takes to complete one full cycle.
• 😀 The period of a mass-spring system depends on the mass and the spring constant, and is given by the formula: T = 2π√(m/k).
• 😀 The period of a pendulum depends on the length of the pendulum and the acceleration due to gravity, and is given by the formula: T = 2π√(L/g).
• 😀 In a mass-spring system, increasing the mass increases the period, as mass is in the numerator of the equation.
• 😀 In a mass-spring system, increasing the spring constant decreases the period, as the spring constant is in the denominator of the equation.
• 😀 For a pendulum, increasing the pendulum length (distance between the center of suspension and the center of mass) increases the period.
• 😀 The period of a pendulum decreases if the acceleration due to gravity increases, as gravity is in the denominator of the equation.
• 😀 A pendulum's period is only affected by amplitude if the amplitude exceeds 15 degrees, in which case the pendulum is no longer in simple harmonic motion and the period equation no longer applies.

Q & A

What is the period in simple harmonic motion?

The period is the time it takes to complete one full cycle of the motion.

What is the symbol for period and what are its typical units?

The symbol for period is a capital 'T', and the typical units are seconds, or seconds per cycle. However, it could also be expressed in minutes, hours, days, fortnights, decades, or even millenniums.

How does the displacement of the object in simple harmonic motion relate to the amplitude?

The maximum displacement from the equilibrium position is called the amplitude, and it represents the maximum distance the object travels from its equilibrium point.

If an object starts at position 1 in simple harmonic motion, what does one full cycle look like?

If the object starts at position 1, it moves to position 2, then to position 3, back to position 2, and finally returns to position 1. This completes one full cycle.

What happens if the object starts at position 2 in simple harmonic motion?

If the object starts at position 2, it could move in either direction. For example, if it moves toward position 3, it would follow the sequence 2, 3, 2, 1, and back to 2 for one full cycle.

What if the object starts at a position between the main positions (1, 2, 3)?

If the object starts between positions 1 and 2, for instance, it must move through both directions (left and right) before completing a full cycle and returning to the starting point while moving in the same direction as at the start.

What is the equation for the period of a mass-spring system?

The period of a mass-spring system is given by the equation: T = 2π * √(m/k), where m is the mass attached to the spring and k is the spring constant.

What factors affect the period of a mass-spring system?

The period of a mass-spring system is affected by the mass (m) attached to the spring and the spring constant (k). Increasing the mass increases the period, while increasing the spring constant decreases the period.

How does the length of the pendulum affect its period?

The period of a pendulum is affected by the length (L) of the pendulum. The longer the pendulum, the greater the period, meaning it takes more time to complete one full cycle.

Does the mass of the pendulum bob affect the period of a pendulum?

No, the mass of the pendulum bob does not affect the period. This is because the mass does not appear in the equation for the period of a simple pendulum.

What happens when the amplitude of a pendulum exceeds 15 degrees?

When the amplitude of a pendulum exceeds 15 degrees, the motion is no longer considered simple harmonic motion, and the period equation for simple harmonic motion no longer applies. The motion remains periodic, but not simple harmonic.

How does changing the acceleration due to gravity affect the period of a pendulum?

The period of a pendulum decreases as the acceleration due to gravity increases. Since gravity appears in the denominator of the period equation, a higher gravity results in a shorter period.