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Transcript
Simple Harmonic Motion Simple Harmonic Motion – Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium. A mass-spring system is an example of simple harmonic motion. Hooke’s Law Spring force = -(spring constant x displacement) Felastic = -kx Hooke’s Law cont. At the equilibrium position, velocity is at maximum, spring force and acceleration are zero. At maximum displacement, spring force and acceleration is a maximum and velocity is at zero. The negative sign in the equation signifies that the direction of the spring force is always opposite the direction of the mass’s displacement. The term k stands for spring constant. A greater value for k means a stiffer spring because a greater force is needed to stretch or compress it. The SI units of k are N/m. Measuring Simple Harmonic Motion For small angles, a pendulum’s motion is simple harmonic. Amplitude – The maximum displacement from equilibrium. Period – The time it takes to execute a complete cycle of motion. Frequency – The number of cycles or vibrations per unit of time. Period and frequency measure time. Frequency is the reciprocal of the period. Cont. Equations: f = 1/T The SI unit of frequency is Hertz (Hz) or 1/s. T = 1/f The SI unit of period is the second (s). Period of a Simple Pendulum The period of a simple pendulum depends on string length and gravity. Equation: T = 2√L/g Period = 2 x square root of (length divided by free-fall acceleration) Period of a Mass-Spring System The period of a mass-spring system depends on mass and the spring constant. Equation: T = 2√m/k Period = 2 x square root of (mass divided by spring constant) Homework Pg. 441 2-3 Pg. 445 1 and 3 Pg. 449 1 and 2 Pg. 451 1 and 2 top of page Pg. 451 1 and 2 bottom of page