Oscillations

Periodic Motion

• def: motion that repeats itself at regular intervals

• ex:

  • rush hour traffic

  • a swing

  • a yo-yo

  • heartbeat

  • breathing

motion that repeats itself at regular intervals

What is the definition of Periodic motion?

frequency (f)

• def: number of oscillations (or cycles) / second (in Hz)

the number of oscillations (or cycles) per second (in Hz)

What is the definition of frequency (f)?

period (T)

• def: time for one complete cycle (in s)

the time it takes for one complete cycle/oscillation (in seconds)

What is the definition of a period (T)?

T = 1/f 

Equation to find the period (T) 

pendulum

• oscillates back and forth

• its position is a sinosoidal function of time

• called a simple harmonic motion (SHM)

an object undergoes simple harmonic motion when the net force acting on it is a linear restoring force

• Remember: an object undergoes simple harmonic motion when the net force acting on it is a linear restoring force

• when the F = -kx

Hooke’s law

• F = -kx

• if a mass is displaced from its equilibrium position and released, it will undergo simple harmonic motion

f = -kx

Equation to find linear restoring force:

the restoring force is the tangential component of the weight (wsinθ)

Remember: the restoring force is the tangential component of the weight (wsinθ)

F = mg sin (θ) = (mg / pendulum length) X (arc length)

Equation to find the magnitude of the restoring force?

θ = arc length (x) / pendulum length (L)

Equation to find the angle θ in a pendulum?

k = mg / L

equation to find k for a pendulum?