Physics: An Introduction Chapter 13 -- Reference Tools & Resources

Chapter 13: Oscillations about Equilibrium
Reference Tools & Resources

Reference Tools & Resources

I. Key Terms and Phrases

periodic motion: motion that repeats itself.

complete cycle: this occurs when both the position and velocity of an oscillating object repeat themselves between two successive passes.

period (for oscillations): the amount of time for one complete cycle.

frequency: the number of cycles per unit of time.

simple harmonic motion: the oscillatory motion that results from a force that obeys Hooke's law.

amplitude: the maximum displacement from equilibrium.

angular frequency: 2p times the frequency.

simple pendulum: a mass suspended by a cord or rod of negligible mass.

physical pendulum: a mass distribution that is suspended and free to oscillate.

damped oscillation: when an oscillating system looses energy.

underdamped oscillation: when a small damping constant causes an oscillating system to decrease in amplitude.

critically damped oscillation: when the damping constant is just large enough to prevent oscillations.

overdamped oscillation: when the damping constant is more than just large enough to prevent oscillations.

driven oscillation: when an external agent forces a system to oscillate.

natural frequency: a frequency at which a system will oscillate if no driving force is applied.

resonance: the phenomenon that large amplitude oscillations occur when a system is driven at its natural frequency.

II. Important Equations

Name/Topic Equation Explanation
frequency The frequency equals the inverse of the period.

simple harmonic motion Position as a function of time in SHM assuming the motion begins at the maximum displacement.

angular frequency w = 2p f The relationship between angular frequency and frequency.

period The period of a mass m oscillating on a spring with force constant k.

mechanical energy The mechanical energy in SHM.

period The period of a simple pendulum of length L.

Name/Topic	Equation	Explanation
frequency		The frequency equals the inverse of the period.
simple harmonic motion		Position as a function of time in SHM assuming the motion begins at the maximum displacement.
angular frequency	w = 2p f	The relationship between angular frequency and frequency.
period		The period of a mass m oscillating on a spring with force constant k.
mechanical energy		The mechanical energy in SHM.
period		The period of a simple pendulum of length L.

III. Know Your Units

Quantity Dimension SI Unit
period [T] s

frequency (f) [T^-1] Hz

angular frequency (w) [T^-1] rad/s

amplitude [L] m

Quantity	Dimension	SI Unit
period	[T]	s
frequency (f)	[T^-1]	Hz
angular frequency (w)	[T^-1]	rad/s
amplitude	[L]	m