CSimple Harmonic Motion and Waves Kinematics of simple harmonic motion: Oscillation: an effect expressible as a quantity that repeatedly and regularly fluctuates above and below a average value, as the pressure of an alternating current. Examples include: • Cycle: One cycle is defined as one complete oscillation of the pendulum (A-B-A) • Equilibrium Position: the position where the pendulum would be at rest when undisturbed (O) • Amplitude (x0): maximum displacement from equilibrium position (OB or OA) – measured in metres. Time Period (T): the length of time to complete one cycle – measured in seconds • Frequency (f): the number of cycles the pendulum makes per unit time – measured in 1/s or hertz (Hz) • Angular frequency (? or 2? f): used when describing circular motion, or even an oscillation in the case of 2? equivalent to one cycle. Displacement: the distance of an oscillating body from its central position or point of equilibrium at any given moment. Amplitude: the absolute value of the maximum displacement from a zero value during one period of an oscillation.
Frequency: the number of periods or regularly occurring events of any given kind in unit of time. This is usually measured in one second. Period: the time taken to complete one cycle of a regularly recurring phenomenon Phase Difference: Simple Harmonic Motion: vibratory motion in a system in which the restoring force is proportional to the displacement from equilibrium. This is expressed by the equation: a = -? ^2x Energy changes during simple harmonic motion (SHM): Kinetic energy = mv^2 /2 and the potential energy at any point = total energy – KE.
Because no energy is lost when the total energy is a constant value, the energy when a body is active sees continual changes between kinetic and potential energy. Forced oscillations and resonance: Damping: The effect in which there is a loss of energy due to the friction in real oscillation. Examples of damping include: • Light damping, critical damping, etc. Natural frequency of vibration Wave Characteristics: Damping: The effect in which there is a loss of energy due to the friction in real oscillation. Examples of damping include: • Light damping, critical damping, etc.
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Natural frequency of vibration Wave Properties: Snell's Law relates the angle of incidence to the angle of refraction to the ratio of the velocity of the wave in the different media, which is always equal. It is stated by: sin i = v1 __________________________________________________________________________ sin r = v2 Diffraction takes place when a wave passes through a small opening. If the op Doppler Effect: The Doppler effect is where there is An change in the frequency of sound, light, or other waves as there is a change in the distance between the source and observer.
The effect causes the sudden change in pitch noticeable in a passing siren, as well as the redshift seen by astronomers. Electrical Currents Electrical potential difference, current and resistence: Electrical potential difference (Voltage) is the electric potential difference between two points — or the difference in electric potential unit of a unit test charge transported between two points. The electron volt is a unit of energy equal to approximately 1. 6? 10? 19 joule (J). It is the amount of energy gained by the charge of a single electron moved across an electric potential difference of one volt.
Thus it is 1 volt (1 joule per coulomb, 1 J/C) multiplied by the electron charge (1e, or 1. 602176565(35)? 10? 19 C). Electric current is the flow of charge (i. e. the + of batteries is charged as it has higher PE and the current flows to -. The unit of current is the amp (A), a scalar quantity. Resistence is the rate at which charge current flow through a conducter is not much allowed. This normally depends on the conducters size and material. It is measured in ohm (? ). It is related to the cross sectional area (A), length (L) and the material and the constant of proportionality is called the resistivity (p).
Hence R = pL/A Ohm's law states that electric current is proportional to voltage and inversely proportional to resistance in terms of flowing across and through it. If the potential difference across a conductor is V and the current flowing through it is I, then according to Ohm's law: V=IR. Ohmic conductor behaviour is demonstrated when graphing I against V of being a straight line Non-ohmic conductor behaviour is demonstrated when graphing I against V of not being a straight line. i. e. ight bulb filaments Electric circuits: Electromotive force (emf) refers to voltage output generated by a battery or by the magnetic force which states that a time varying magnetic field will induce an electric current. Internal resistence is the resistence of that of all cells that are made from materials that have resistance. If such a cell was connected to a resistor, there is less energy to be converted to heat in the resistor and the potential difference across it less then the cell's emf. With Oh
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