Preview
IB DP Physics — Unit C: Wave Behaviour | SL & HL | C.1 Simple Harmonic Motion
📋 What You Will Learn
- Observe and describe the oscillatory motion of a mass on a spring and a simple pendulum using real-world physical setups
- Define all key quantities — displacement, amplitude, period, frequency, angular frequency, and spring constant — with correct notation and units
- Derive the period equations \( T = 2\pi\sqrt{m/k} \) and \( T = 2\pi\sqrt{L/g} \) step-by-step from Newton's second law and free body analysis
- Apply the equations for period and energy to solve figure-based and graph-based problems
- Analyse how kinetic energy and potential energy vary with displacement throughout one complete oscillation
- Evaluate common misconceptions about what affects the period of oscillation and connect SHM to the wider IB Physics course
🌍 Real-World Context A child on a playground swing, the pendulum of a grandfather clock, the suspension system of a car absorbing a road bump, the vibrating string of a guitar — all of these systems share a remarkable property: they oscillate back and forth with a remarkably steady rhythm. The time it takes for one complete swing of a grandfather clock's pendulum does not change whether the pendulum swings through a large arc or a tiny one. This isochronous behaviour — the independence of period from amplitude — puzzled and fascinated scientists for centuries, and it is the key to understanding why pendulum clocks keep accurate time. In this topic, we will uncover the physical reason for this behaviour by analysing the forces acting on oscillating systems.
🔍 Guiding Question What physical conditions must be satisfied for a system to undergo simple harmonic motion, and how do the mass–spring system and the simple pendulum each satisfy those conditions? How does energy transform between kinetic and potential forms during oscillation, and what determines the period of each system?
Physical Setup: The Mass–Spring System
Imagine a metal block hanging from a coiled spring that is fixed to a ceiling. When the block is at rest, it hangs at a position where the upward spring force exactly balances the downward weight — this is the equilibrium position. Now pull the block downward by a small distance and release it. The block accelerates upward, passes through equilibrium, overshoots, decelerates, stops momentarily above equilibrium, then returns downward again. This repeating back-and-forth motion is what we call oscillation.
The key observation is that the block always returns toward the equilibrium position — there is always a force pulling it back. This force is called the restoring force, and it is the defining feature of simple harmonic motion. The greater the displacement from equilibrium, the stronger the restoring force pulling the block back.
Notice from the diagram that at maximum displacement (either +A or −A), the restoring force is at its greatest, so the acceleration is at its maximum. At the equilibrium position, the net force is zero, so the acceleration is zero — but the velocity is at its maximum because the block has been accelerating toward this point throughout its journey. This interplay between force, acceleration, and velocity is the heart of SHM.
Core Concepts and Definitions — Mass–Spring System
As the block oscillates, we need a precise way to describe its position at any moment. We measure displacement from the equilibrium position — positive in one direction, negative in the other. The maximum displacement reached in either direction is called the amplitude. The time for one complete oscillation (one full cycle back to the starting position with the same velocity) is the period.
📖 Key Definition — Displacement in SHM The displacement \( x \) in SHM is the distance of the oscillating object from its equilibrium position, measured along the direction of motion. It is a vector quantity — positive in one direction, negative in the other. SI unit: metres (m).
📖 Key Definition — Amplitude The amplitude \(