Problem 67 - Algebra and Trigonometry

Question

What is simple harmonic motion? Give an example with your description.

Step-by-Step Solution

Answer

Simple Harmonic Motion (SHM) is a type of oscillatory motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Characteristics of SHM include perpetual motion about a fixed point, highest velocity at equilibrium, and greatest acceleration at maximum displacement. A practical example of SHM is the motion of a simple pendulum.

Step 1: Definition of Simple Harmonic Motion

Simple Harmonic Motion, abbreviated as SHM, is a type of oscillatory or periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. This can be mathematically represented as \(F = -kx\) where: \(F\) is the restoring force, \(x\) is the displacement from the equilibrium position and \(k\) is a constant.

Step 2: Characteristics of Simple Harmonic Motion

Characteristics of SHM are: 1. The motion is always about a fixed point called the center of motion or equilibrium point, 2. The motion is perpetual unless an external force interferes, 3. The velocity of the object in SHM is highest when it passes the equilibrium point and is zero when it reaches the maximum displacement, 4. The acceleration of the object is highest at the maximum displacement and zero at the equilibrium point.

Step 3: Example of Simple Harmonic Motion

One typical example of simple harmonic motion is a simple pendulum. When a pendulum is displaced from its equilibrium position and released, it swings back and forth due to the restoring force of gravity. The restoring force of the pendulum is proportional to its displacement (represented by the angle) and acts in the opposite direction, making the pendulum's to-and-fro motion a Simple Harmonic Motion.