oscillations_02 - oscillations_02 1 Oscillations Time...

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1 Oscillations oscillations_02 CP Ch 14 How can you determine the mass of a single E-coli bacterium or a DNA molecule ? CP458 Time variations that repeat themselves at regular intervals - periodic or cyclic behaviour Examples: Pendulum (simple); heart (more complicated) Terminology: Amplitude : max displacement from equilibrium position [m] Period : time for one cycle of motion [s] Frequency : number of cycles per second [s -1 = hertz (Hz)] shm_v.avi SHM
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2 Signal from ECG period T Period : time for one cycle of motion [s] Frequency : number of cycles per second [s -1 = Hz hertz] CP445 1 kHz = 10 3 Hz 10 6 Hz = 1 MHz 1GHz = 10 9 Hz time voltage
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3 Example: oscillating stars Brightness Time CP445
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4 oscillations_02: MINDMAP SUMMARY Reference frame (coordinate system, origin, equilibrium position), displacement (extension, compression), applied force, restoring force, gravitational force, net (resultant) force, Newton’s Second Law, Hooke’s Law, spring constant (spring stiffness), equilibrium, velocity, acceleration, work, kinetic energy, potential energy (reference point), gravitational potential energy, elastic potential energy, total energy, conservation of energy, ISEE, solve quadratic equations, SHM, period, frequency, angular frequency, amplitude, sine function (cos, sin), phase, phase angle, radian, SHM & circular motion 2 1 2 2 2 2 2 2 max max 1 cos 2 cos( ) sin( ) cos( ) 1 1 2 2 2 1 1 1 2 2 2 e r e G e G r e dr dv v a F ma F k x F k x dt dt W F dr U k x U m g h E K U U x A t v A t a x A t x k m f T f T T f m T k E K U mv k x k A θ ϖ π = = = = = - = = = = + + = = - = - = = - = = = = = = = + = = = r r r r r r r r max A x
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5 Simple harmonic motion SHM object displaced, then released objects oscillates about equilibrium position motion is periodic displacement is a sinusoidal function of time ( harmonic) T = period = duration of one cycle of motion f = frequency = # cycles per second restoring force always acts towards equilibrium position amplitude – max displacement from equilibrium position x e F spring restoring force e F k x = - CP447 x = 0 +X
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6 Click the image to view the animation of the two objects executing SHM.
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oscillations_02 - oscillations_02 1 Oscillations Time...

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