How is resonance related to harmonic motion?

Resonance is a phenomenon that occurs when an object vibrates at its natural frequency.

When an object is subjected to a periodic force that matches its natural frequency, resonance occurs. This causes the amplitude of the object's vibrations to increase significantly. The energy of the periodic force is transferred to the object, causing it to vibrate with greater amplitude. This is known as forced vibration.

Harmonic motion is a type of motion that occurs when an object vibrates at a frequency that is an integer multiple of its natural frequency. This type of motion is characterized by a sinusoidal waveform and is often referred to as simple harmonic motion.

Resonance is closely related to harmonic motion because both phenomena involve the vibration of an object at a specific frequency. In the case of resonance, the object is subjected to a periodic force that matches its natural frequency, causing it to vibrate with greater amplitude. In the case of harmonic motion, the object vibrates at a frequency that is an integer multiple of its natural frequency, resulting in a sinusoidal waveform.

In summary, resonance and harmonic motion are closely related because they both involve the vibration of an object at a specific frequency. Resonance occurs when an object is subjected to a periodic force that matches its natural frequency, while harmonic motion occurs when an object vibrates at a frequency that is an integer multiple of its natural frequency.