Unit D: Oscillatory Motion & Mechanical Waves Simple Harmonic MOtion

Simple Harmonic Motion (SHM) Oscillatory Motion: motion in which the period of each cycle is constant Simple Harmonic Motion (SHM): motion that repeats itself over the same path Example: mass on a spring or pendulum

Hooke’s Law Equilibrium: The position where motion will come to rest Restoring Force (elastic force): when a spring is stretched or compressed, this force always acts in the direction of the equilibrium Hooke’s Law says the restoring force is directly proportional to the displacement (x) of the mass from the equilibrium position

Hooke’s Law The bigger the k value, the stiffer the spring will be Since F = ma, SHM is motion where the acceleration is directly proportional to the restoring force Hooke’s law and Newton’s 2nd law can be equated to one another and you can calculate the acceleration of a mass:

Terms Displacement: The distance of the object from the equilibrium position.   Amplitude: Maximum displacement from the equilibrium position. Cycle: One complete back and forth motion Period: Time to make one cycle (seconds/cycle) Frequency: Number of cycles per unit of time (cycles/second)

Sample Problem A 0.40 kg mass is vibrating at the end of a horizontal spring along a frictionless surface. If the spring constant is 6.0 N/m, what is the restoring force acting on the mass when it is 0.070 m from its equilibrium position? (F = 0.42N)

Sample Problem A weight of 4.6 N will stretch a vertical spring 0.048 m. What is the spring constant? (k=95.0N/m)

Restoring Force & Pendulums The restoring force acting on a pendulum is: FR

Sample Problem Determine the restoring force on a 100 g mass pulled to the side to an angle of 10.0º from the vertical. (F=0.170N)

Homework p. 151 #1-10