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Frequency and Period of SHM

Isabella Lopez

Isabella Lopez

7 min read

Study Guide Overview

This study guide covers Simple Harmonic Motion (SHM), focusing on frequency, period, and their inverse relationship. It explores object-spring oscillators, where the period depends on mass and spring constant, and simple pendulums, where the period depends on length and gravity. Key formulas, relationships between variables, and conceptual understanding are emphasized, along with practice questions covering both multiple-choice and free-response formats.

AP Physics 1: Simple Harmonic Motion (SHM) - The Night Before ๐Ÿš€

Hey! Let's get you ready to ace this exam! We're going to break down Simple Harmonic Motion (SHM) into bite-sized pieces. Remember, you've got this! ๐Ÿ’ช

Introduction to SHM

SHM is all about things that oscillate or repeat their motion. Think of a swing, a spring, or a pendulum. We'll focus on frequency and period, which are key to understanding these movements. Let's dive in!

Frequency and Period Basics

  • Period (T): The time it takes for one complete cycle or oscillation. Measured in seconds (s). ๐Ÿ”„
  • Frequency (f): The number of cycles or oscillations per second. Measured in Hertz (Hz), where 1 Hz = 1 sโปยน.
Key Concept

Inverse Relationship: Frequency and period are inversely related. As one goes up, the other goes down. Mathematically: f=1Tf = \frac{1}{T} or T=1fT = \frac{1}{f}

* **Example:** If a system has a frequency of 4 Hz, its period is 0.25 s.
Memory Aid

Think of it like this: Frequency is how frequently something happens, and Period is the time it takes to happen once. They're two sides of the same coin! ๐Ÿช™

Object-Spring Oscillators

Period of a Spring-Mass System

  • An object-spring oscillator involves a mass (m) attached to a spring, oscillating back and forth.
  • The spring constant (k) measures the stiffness of the spring. Higher k means a stiffer spring.
Key Concept

The period (T) of this system is determined by both the mass (m) and spring constant (k). The formula is: T=2ฯ€mkT = 2\pi \sqrt{\frac{m}{k}}

  • Mass (m) and Period (T): Direct relationship. More mass = longer period.
  • Spring Constant (k) and Period (T): Inverse relationship. Stiffer spring = shorter ...
Previous Topic - Defining Simple Harmonic Motion (SHM)Next Topic - Representing and Analyzing SHM

Question 1 of 8

If an object oscillates with a frequency of 2 Hz, what is its period? โฑ๏ธ

0.5 s

1 s

2 s

4 s