Atlas MCAT Course
Physical Foundations → Oscillations & Simple Harmonic Motion
Oscillations & Simple Harmonic Motion
Where energy continuously trades forms.
01The idea
Oscillatory motion appears everywhere: springs and pendulums, sound waves, molecular vibrations, and biological rhythms (heartbeats, breathing patterns). What unifies them is not the object — it’s the force law.
This creates predictable, repeating motion.
THREAD · Energy vs. rate
02Build the model
AThe defining feature of SHM
SHM exists if there is an equilibrium position, displacement from equilibrium creates a restoring force, the restoring force points toward equilibrium, and the restoring force increases with displacement. This is why springs and small-angle pendulums oscillate.
BRestoring force → motion
In SHM, force is zero at equilibrium, force is maximal at extreme displacement, and acceleration always points toward equilibrium.
This single idea solves many questions.
CEnergy view of oscillations (high-yield)
SHM is best understood using energy. Throughout the motion, total mechanical energy is constant, and energy oscillates between potential and kinetic. At the extremes, potential energy is maximum and kinetic energy is zero. At equilibrium, kinetic energy is maximum and potential energy is at its minimum.
DPeriod and frequency: timing the motion
Two quantities describe timing: the period (T), the time for one full cycle, and the frequency (f), cycles per second. They are inversely related: faster oscillation means a shorter period.
EWhat determines the period?
This is crucial and testable. For ideal SHM, the period depends on restoring strength and on inertia, and does not depend on amplitude. A stiffer spring oscillates faster; a larger mass oscillates more slowly.
FPhase: where you are in the cycle
Phase describes position within the oscillation cycle. Two oscillators can have the same frequency and be out of phase. This matters later for wave interference and superposition.
GDamping: real systems lose energy
Real oscillators experience friction, air resistance, and internal losses. With damping, energy decreases over time and amplitude shrinks, while frequency is mostly unchanged (for light damping).
HResonance: driving at the right frequency
If an external force drives an oscillator at its natural frequency, energy transfer is maximized. This is resonance.
This directly connects to hearing, instrument acoustics, and structural failure examples.
IConnecting SHM to waves (preview)
Waves are many oscillators, coupled together, transmitting energy. Understanding SHM makes waves trivial.
03See the connections
The lesson names these links itself. Read the map left to right.
Cause
- Restoring force ∝ displacement
- Points to equilibrium
Behavior
- PE ↔ KE exchange
- Period set by stiffness and mass, not amplitude
Real systems
- Damping drains energy
- Resonance maximizes transfer
- Coupled oscillators → waves
Next: waves and harmonics.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
Where in its motion does a mass on a spring move fastest?
Think first.
You pull an ideal spring–mass system farther before releasing it. What happens to its period?
Think first.
The mass on a spring is doubled. What happens to the oscillation?
Think first.
A lightly damped pendulum swings for a while. What changes over time?
05MCAT lens
Predict the direction
Increase mass → slower oscillation
Increase stiffness → faster oscillation
Increase amplitude → more energy, same period
Maximum speed → equilibrium position
No equations required to get most answers.
06Common traps
Trap 1: Maximum speed at extremes
Misconception
Wrong.
Correct model
Speed max at equilibrium.
Trap 2: Amplitude affects period
Misconception
Wrong (ideal SHM).
Correct model
Period independent of amplitude.
Trap 3: Damping stops oscillation instantly
Misconception
Wrong.
Correct model
Energy decays gradually.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
What defines SHM
Check against 02 · A: a restoring force proportional to displacement.
How force relates to displacement
Check against 02 · B: zero at equilibrium, maximum at extremes.
How energy moves during oscillation
Check against 02 · C: PE ↔ KE with constant total.
Why resonance occurs
Check against 02 · H: driving at the natural frequency.
If something feels unclear, the missing idea is usually thisSHM is motion created by a linear restoring force and conserved energy exchange.
08Remember
REMEMBER · if you keep only a few things
- SHM needs a restoring force proportional to displacement.
- Speed max at equilibrium; force max at extremes.
- Energy trades between PE and KE; the total is constant.
- Period depends on stiffness and mass, not amplitude.
- Damping drains energy, not periodicity.
- Resonance: drive at the natural frequency.
09Forward hook
Now that oscillations are clear, the natural extension is waves and harmonics: oscillations that propagate through space.
What happens when oscillations are coupled so energy moves through space?
That leads to waves and harmonics.
Next lessonWaves & Harmonics→