Simple Harmonic Motion PDF

QUARTER 2: PHYSICS 10 Simple Harmonic Motion SIMPLE HARMONIC MOTION Introduction to Periodic Motion Time can be measured either by duration or periodic motion. Early clocks measured duration by tracking consistent processes like the burning of incense or t...

QUARTER 2: PHYSICS 10 Simple Harmonic Motion SIMPLE HARMONIC MOTION Introduction to Periodic Motion Time can be measured either by duration or periodic motion. Early clocks measured duration by tracking consistent processes like the burning of incense or the flow of sand. Periodic motion is foundational to our modern understanding of time: years are marked by the sun's motion, months by the moon, days by Earth’s rotation, hours by gears, and seconds by the oscillations of springs or pendulums. Today, a second is precisely defined by the specific frequency of radiation from cesium 133 atoms. Sundials relied on the sun's movement, while mechanical clocks used escapements to transform continuous movement into discrete steps. In the 17th century, Christian Huygens refined the use of pendulums, improving clock accuracy. Later, Robert Hooke's discovery of spring oscillations further advanced timekeeping. By the 18th century, William Harrison’s innovations allowed for clocks accurate to within a second over a century. One of the most important examples of periodic motion is simple harmonic motion (SHM). Simple Harmonic Motion Imagine a physical system consisting of a block of mass 𝑚 attached to the end of a spring, where the block can move freely on a horizontal, frictionless surface. When the spring is neither stretched nor compressed, the block sits at the system's equilibrium position. Experience tells us that if the block is displaced from this position, it will oscillate back and forth. We can qualitatively understand the motion shown in Figure 1 by noting that when the block is moved a small distance 𝑥 from equilibrium, the spring exerts a force on the block that is proportional to this displacement, as described by Hooke's law: 𝐹 = −𝑘𝑥 Figure 1. A block attached to a spring moving on a frictionless surface. (a) When the block is displaced to the right of equilibrium (x 0), the force exerted by the spring acts to the left. (b) When the block is at its equilibrium position (x 0), the force exerted by the spring is zero. (c) When the block is displaced to the left of equilibrium (x 0), the force exerted by the spring acts to the right. CLSU Laboratory for Teaching and Learning QUARTER 2: PHYSICS 10 Simple Harmonic Motion This force is known as a restoring force because it always acts toward the equilibrium position, opposing the displacement. For example, when the block is displaced to the right of 𝑥 = 0 in Figure 1, the displacement is positive, and the restoring force points to the left. Conversely, when the block is displaced to the left of \( x = 0 \), the displacement is negative, and the restoring force points to the right. Simplified Concepts of SHM Simple harmonic motion (SHM) is a type of periodic motion. Two simple systems of SHM that are mainly discussed in college are an ideal spring and a simple pendulum. But before discussing these 2 systems, it is essential to go over periodic motion first. Periodic motion or oscillation refers to kinds of motion that repeat themselves over and over. For example, a clock pendulum. Understanding periodic motion is critical for understanding more complicated concepts like mechanical waves (e.g. sound) and electromagnetic waves (e.g. light) Oscillation is characterized by an equilibrium and a restoring force. At equilibrium, restoring force on the object is zero. When the object is displaced from equilibrium, a restoring force acts on the object to restore its equilibrium. When the restoring force is directly proportional to displacement from equilibrium, the oscillation is called simple harmonic motion (SHM). Important characteristics of any periodic motion: Amplitude (A) is maximum magnitude of displacement from equilibrium Period (T) is the time to complete one cycle (unit: s) Frequency (f) is the number of cycles in a unit of time (unit: s-1) 1 1 Period and frequency are related by the following relationship: 𝑇 = 𝑜𝑟 𝑓 = 𝑓 𝑇 Angular frequency (ω): 𝜔=2𝜋𝑓 Two Basic Examples of SHM Simple Pendulum Elastic Spring will be discussed on our face-to-face classes along with the formula and computations. CLSU Laboratory for Teaching and Learning