← Physics I: Mechanics

Unit 15: Oscillations

Simple harmonic motion, the pendulum, and what damping and driving do to an oscillator left alone versus pushed on purpose.

6 topics · 21 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Simple Harmonic Motion

  1. How it worksHow does a restoring force proportional to displacement guarantee sinusoidal motion in time?
  2. Worked exampleFind the period of a 0.5 kg mass on a spring with k = 20 N/m.
  3. Common mistakeWhy isn't the period of a mass on a spring affected by how far you first pull it back before releasing it?
Your turn1 of 2
A 2.15 kg mass is attached to a spring with spring constant 41 N/m. What is the period of its oscillation, in seconds?

Position, Velocity, and Acceleration in SHM

  1. How it worksHow do position, velocity, and acceleration in SHM all trace out sine and cosine curves shifted from each other?
  2. Worked exampleFind the maximum speed of a mass in SHM with amplitude 0.1 m and angular frequency 5 rad/s.
  3. Going furtherWhat happens to the maximum acceleration of an oscillator if you double its amplitude but keep its frequency fixed?
Your turn1 of 2
A mass oscillates in SHM with amplitude 0.224 m and angular frequency 8 rad/s. What is its maximum speed, in meters per second?

Energy in Simple Harmonic Motion

  1. How it worksHow does energy trade between kinetic and elastic potential while the total stays fixed throughout an oscillation?
  2. Worked exampleFind the total mechanical energy of a 2 kg mass on a spring with k = 50 N/m and amplitude 0.3 m.
  3. Common mistakeWhy doesn't a mass on a spring at maximum displacement have zero total energy just because it's momentarily at rest?
Your turn1 of 2
A 3.63 kg mass oscillates on a spring with k = 72 N/m and amplitude 0.473 m. What is the total mechanical energy of the system, in joules?

The Simple Pendulum

  1. How it worksHow does the small-angle approximation turn a pendulum's motion into the same equation as a mass on a spring?
  2. Worked exampleFind the period of a simple pendulum of length 2 m, taking g = 9.8 m/s2.
  3. Worked exampleFind the length of a pendulum with a period of exactly 1 second on Earth.
  4. Common mistakeWhy doesn't the mass of a pendulum's bob affect its period at all?
  5. Going furtherWhat happens to a pendulum's period once its swing angle grows too large for the small-angle approximation to hold?
Your turn1 of 2
What is the period of a simple pendulum of length 2.88 m, taking g = 9.8 m/s2?

Damped Oscillations

  1. How it worksHow does a drag-like force proportional to velocity steadily drain energy from an oscillator over each cycle?
  2. Common mistakeWhy doesn't damping change how fast an oscillator swings back and forth, at least until it's damped very heavily?
  3. Going furtherWhat happens to an oscillator's motion once damping becomes so strong that it never actually oscillates?
Your turn1 of 2
A lightly damped oscillator (weak damping) is compared to the same oscillator with no damping at all. How does the time for one swing (the period) compare between them?

Driven Oscillations and Resonance

  1. How it worksHow does driving an oscillator at its natural frequency pump in energy every single cycle instead of canceling out?
  2. Worked exampleFind the natural frequency of a 1 kg mass on a spring with k = 100 N/m.
  3. Common mistakeWhy doesn't pushing an oscillator harder always make it swing with a bigger amplitude?
  4. Ties togetherHow does resonance in a mechanical oscillator connect to the same phenomenon that lets a radio tune to one station?
Your turn1 of 2
A 2.94 kg mass is attached to a spring with spring constant 137 N/m. What is the natural frequency of oscillation, in hertz?