Simple Harmonic Motion [Part-I]

Simple Harmonic Motion (SHM)

A type of periodic motion where acceleration and net force are proportional to displacement and act in the opposite direction.

Simple Harmonic Oscillator

A system that oscillates with SHM, e.g., a mass attached to a spring on a frictionless surface.

x = 0; where the spring is neither stretched nor compressed.

What position is defined as equilibrium in SHM with a spring?

Amplitude (A)

The maximum displacement from equilibrium. Units depend on the type of oscillation (meters for a spring system).

It accelerates toward equilibrium, reaching maximum velocity at x = 0, then continues to -A, repeating in SHM.

What happens when a mass attached to a spring is released from x = A?

As it passes through the equilibrium position.

Where does the maximum speed of the mass occur in SHM?

A stiffer spring (larger k) results in a shorter period (faster oscillation).

How does spring stiffness (k) affect the period T?

A larger mass increases the period, causing slower oscillation.

How does mass (m) affect the period T?

The mass (m) of the object and the spring constant (k)

Which two factors affect the period of SHM?

No, period and frequency are independent of amplitude.

Does amplitude affect the period or frequency of SHM?

Hooke’s law

The law that describes the restoring force in SHM with a spring.

Fs = -kx

Mathematical representation of the Hooke’s law

It shows that the restoring force always acts opposite to displacement.

What is the significance of the negative sign in Hooke’s law?

Meters (m)

Units of displacement and amplitude in a spring system

Example of SHM in music.

A guitar string vibrates at the same frequency whether plucked gently or hard.

Example of SHM with stiffness.

A diving board vibrates faster (shorter period) when stiff, and slower (longer period) when flexible.

Example of SHM with mass.

A heavy person bounces more slowly on a diving board than a lighter person.