Definition and Characteristics of Simple Harmonic Motion (SHM)
Defining SHM, its conditions (restoring force proportional to displacement), and its relation to uniform circular motion.
What is Definition and Characteristics of Simple Harmonic Motion (SHM)?
A type of periodic motion where the restoring force (and hence acceleration) is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
Key formula / rule: Acceleration in SHM
Key points
- Define Simple Harmonic Motion (SHM).
- Identify the conditions required for SHM.
- Distinguish SHM from other types of oscillatory motion.
- Relate SHM to uniform circular motion.
Common exam trap
Confusing periodic motion with SHM (all SHM is periodic, but not all periodic motion is SHM).
Definitions
- Term
Simple Harmonic Motion (SHM)
- Meaning
A type of periodic motion where the restoring force (and hence acceleration) is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.
- Term
Amplitude (A)
- Meaning
The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
- Term
Time Period (T)
- Meaning
The time taken for one complete cycle of oscillation.
- Term
Frequency (f)
- Meaning
The number of complete cycles of oscillation per unit time.
- Term
Angular Frequency (ω)
- Meaning
A measure of the rate of angular displacement, related to frequency by ω = 2πf. Its unit is radians per second.
- Term
Restoring Force
- Meaning
A force that always acts to bring a system back to its equilibrium position.
Learning objectives
Define Simple Harmonic Motion (SHM).
Identify the conditions required for SHM.
Distinguish SHM from other types of oscillatory motion.
Relate SHM to uniform circular motion.
Understand the key characteristics of SHM: amplitude, frequency, time period, and angular frequency.
Formulae
- Name
Acceleration in SHM
- Note
ω is angular frequency, x is displacement from mean position. Negative sign indicates acceleration is opposite to displacement.
- Expression
a = -ω²x
- Name
Restoring Force in SHM
- Note
k is the force constant (or spring constant). F is directly proportional to displacement and opposite in direction.
- Expression
F = -kx
- Name
Angular Frequency (Mass-Spring System)
- Note
k is the force constant, m is the mass.
- Expression
ω = √(k/m)
- Name
Angular Frequency (Simple Pendulum)
- Note
g is acceleration due to gravity, l is length of the pendulum. Valid for small angular displacements.
- Expression
ω = √(g/l)
- Name
Time Period
- Note
Time taken for one complete oscillation.
- Expression
T = 2π/ω
- Name
Frequency
- Note
Number of oscillations per unit time.
- Expression
f = 1/T = ω/2π
Prerequisites
Basic concepts of motion (displacement, velocity, acceleration).
Understanding of periodic and oscillatory motion.
Newton's Laws of Motion.
Uniform Circular Motion.
Common mistakes
Confusing periodic motion with SHM (all SHM is periodic, but not all periodic motion is SHM).
Ignoring the negative sign in the acceleration equation, which signifies the direction of the restoring force.
Assuming SHM for large oscillations of a pendulum.
Incorrectly relating amplitude, frequency, and time period.
Keywords
Simple Harmonic Motion
SHM
Oscillatory Motion
Periodic Motion
Restoring Force
Amplitude
Time Period
Frequency
Angular Frequency
Uniform Circular Motion
Mass-Spring System
Simple Pendulum
Practice preview
The time period of a simple pendulum is T. If its length is doubled, its new time period will be:…
easy
A body is oscillating with SHM. Its total energy is E. What is the kinetic energy when its displacement is half of the amplitude?…
medium
A system is undergoing SHM. If the amplitude is A and the total energy is E. Which of the following statements is correct regarding the kinetic energy (KE) and potential energy (PE) at displacement x = A/√2?…
hard