15 Oscillations
15 Chapter Review
Key Terms
- amplitude (A)
- maximum displacement from the equilibrium position of an object oscillating around the equilibrium position
- critically damped
- condition in which the damping of an oscillator causes it to return as quickly as possible to its equilibrium position without oscillating back and forth about this position
- elastic potential energy
- potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring
- equilibrium position
- position where the spring is neither stretched nor compressed
- force constant (k)
- characteristic of a spring which is defined as the ratio of the force applied to the spring to the displacement caused by the force
- frequency (f)
- number of events per unit of time
- natural angular frequency
- angular frequency of a system oscillating in SHM
- oscillation
- single fluctuation of a quantity, or repeated and regular fluctuations of a quantity, between two extreme values around an equilibrium or average value
- overdamped
- condition in which damping of an oscillator causes it to return to equilibrium without oscillating; oscillator moves more slowly toward equilibrium than in the critically damped system
- period (T)
- time taken to complete one oscillation
- periodic motion
- motion that repeats itself at regular time intervals
- phase shift
- angle, in radians, that is used in a cosine or sine function to shift the function left or right, used to match up the function with the initial conditions of data
- physical pendulum
- any extended object that swings like a pendulum
- resonance
- large amplitude oscillations in a system produced by a small amplitude driving force, which has a frequency equal to the natural frequency
- restoring force
- force acting in opposition to the force caused by a deformation
- simple harmonic motion (SHM)
- oscillatory motion in a system where the restoring force is proportional to the displacement, which acts in the direction opposite to the displacement
- simple harmonic oscillator
- a device that oscillates in SHM where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement
- simple pendulum
- point mass, called a pendulum bob, attached to a near massless string
- stable equilibrium point
- point where the net force on a system is zero, but a small displacement of the mass will cause a restoring force that points toward the equilibrium point
- torsional pendulum
- any suspended object that oscillates by twisting its suspension
- underdamped
- condition in which damping of an oscillator causes the amplitude of oscillations of a damped harmonic oscillator to decrease over time, eventually approaching zero
Key Equations
| Relationship between frequency and period | [latex]f=\frac{1}{T}[/latex] |
| Position in SHM with [latex]\varphi =0.00[/latex] | [latex]x(t)=A\,\text{cos}(\omega t)[/latex] |
| General position in SHM | [latex]x(t)=A\text{