Simple Harmonic Motion and Its Equation
Oscillation in which the restoring force is proportional to displacement and directed towards the mean position, a = -w2 x, with solution x = A sin(wt + p).
What is Simple Harmonic Motion and Its Equation?
Oscillation in which the restoring force is proportional to displacement and directed towards the mean position, a = -w2 x, with solution x = A sin(wt + p).
Key formula / rule: a = -w2 x defines SHM; T = 2 π/w.
Key points
- Derive the displacement, velocity and acceleration relations for SHM.
- Identify whether a given motion is simple harmonic.
Common exam trap
Calling any periodic motion simple harmonic.
Definitions
- Term
Simple Harmonic Motion and Its Equation
- Meaning
Oscillation in which the restoring force is proportional to displacement and directed towards the mean position, a = -w2 x, with solution x = A sin(wt + p).
- Term
Simple Harmonic Motion and Its Equation — explanation
- Meaning
SHM is the small-oscillation limit of almost every stable system, which is why it recurs across mechanics, sound and circuits. Velocity leads displacement by a quarter cycle and acceleration is out of phase with displacement.
Learning objectives
Derive the displacement, velocity and acceleration relations for SHM.
Identify whether a given motion is simple harmonic.
Formulae
- Key point
a = -w2 x defines SHM; T = 2 π/w.
- Key point
v = w √(A2 - x2); v is maximum at the mean position.
- Key point
Acceleration is maximum at the extremes and zero at the centre.
Prerequisites
PHY-U1-KIN-T2-S2-C2
PHY-U1-NLM-T1-S1-C2
Common mistakes
Calling any periodic motion simple harmonic.
Confusing angular frequency w with frequency f.
Keywords
Simple
Harmonic
Motion
Equation
Practice preview
A particle executes SHM with a displacement given by x(t) = 5 cos(4πt + π/4) meters. What is its maximum velocity?…
medium
The displacement of a particle executing Simple Harmonic Motion (SHM) is given by x = A sin(wt + p). What do A, w, and p represent, respectively?…
easy
If the time period of a particle executing Simple Harmonic Motion (SHM) is 2 seconds, what is its angular frequency?…
easy