Simple Harmonic Motion Physics Mr Berman Periodic Motion

Simple Harmonic Motion Physics Mr. Berman

Periodic Motion

Periodic Motion http: //www. cleonis. nl/physics/inertosc_img/har monic_oscillation. gif

Simple Harmonic Motion: 1. Is a periodic motion that repeats at constant frequency. 2. Has a restoring force that acts to restore the oscillator to equilibrium. F=-kx Hooke’s Law x: displacement from equilibrium

Characteristic Quantities of Simple Harmonic Motion • Displacement: distance from equilibrium. • Amplitude: maximum displacement

Characteristic Quantities of Simple Harmonic Motion • Frequency: oscillations per unit time – Unit: 1/sec =Hertz • Period: time to complete one oscillation – Unit: sec f=1/T T=1/f

Simple Harmonic Motion • Velocity: – maximum as it passes through equilibrium – zero as it passes through the extreme positions in its oscillation. • Acceleration: a=F/m = -kx/m -maximum at extreme points -zero at equilibrium

Mass on a Spring http: //www. walter-fendt. de/ph 14 e/springpendulum. htm

Position vs Time Graph of Mass on Spring x (Sine Curve) a)What is the amplitude? b)What is the period? c) What total distance does the particle travel in one period?

Period of A Spring Mass Oscillator ____ • T=2 p√m/k • m mass • k spring constant

Problem • Calculate the period of a mass of 5 kg on a spring that has a spring constant of 20 N/m. • Answer: 3 s

Question • If you had a spring-mass system on the moon, would the period be the same or different than that of this system on the earth?

Harmonic Motion of a Pendulum • Applets: • • http: //www. walter-fendt. de/ph 14 e/pendulum. htm http: //www 3. interscience. wiley. com: 8100/legacy/college/halliday/0471320005/simulati ons 6 e/index. htm? newwindow=true L

Harmonic Motion of a Pendulum • http: //www 3. interscience. wiley. com: 8100/legacy/college/halliday/0471320005/simulati ons 6 e/index. htm? newwindow=true • Period ___ T=2 p√L/g g=10 m/s 2 L=length of string L

Problem • Calculate the Period of a pendulum of length 0. 75 m. Answer: 1. 7 s

Question • If you had a pendulum on the moon would its period be the same or different compared to the same pendulum on the earth?

Questions • Does the period of a pendulum depend on the mass of the bob? • If you increase the length of the pendulum string, what happens to the period?

Calculating k from a F vs x Graph k is the slope of a F vs x graph