Simple Harmonic Motion Physics 12

Joke of the day: Is it June yet?

Simple Harmonic Motion: Any motion that repeats itself precisely over equal periods of time is called periodic motion If that periodic motion is generated by a linear restoring force then it is simple harmonic motion (SHM).

SHM Examples:

Review: Period (T) is the time for one complete oscillation. Unit = seconds Frequency (f) is the number of complete oscillations per second. Units = Hertz (s-1 or 1/seconds)

Restoring force: will tend to bring the system back toward equilibrium. is a function only of position of the mass or particle. is always directed back toward the equilibrium position of the system. Photo by Mark Tippens A TRAMPOLINE exerts a restoring force on the jumper that is directly proportional to the average force required to displace the mat.

More SHM: Displacement: distance from equilibrium. Amplitude: maximum displacement

F = -kx Review: Hooke’s Law: F =restoring force of spring (N) (-) because the force acts in opposite direction of the displacement and the applied force K = spring constant (N/m) Each spring has it’s own constant x = distance that the spring has been extended or compressed (m) F = -kx

The amplitude, A, of a wave is the same as the displacement ,x, of a spring. Both are in meters. CREST Equilibrium Line Trough Springs are like Waves!

Review: Elastic Potential Energy: Symbol: Ee k = spring constant (N/m) X= length of extension or compression (m) Units = N·m or J Ee = ½ kx2

Conservation of Energy in Springs:

Total energy of mass and spring system: At any position (x) the total energy is: At either end, the mass stops, so velocity =0, also all elastic potential energy At equilibrium, x=0 so all kinetic energy

Period of mass on spring:

Example 1: If you stretch a spring a distance of 12.0cm from its rest length and release it. A 125g mass on the end of the spring completes exactly 20 cycles in 15.5 seconds. Find The period The force constant of the spring The total energy of the system The maximum speed of the mass The speed of the mass when it is 10.0cm from the equilibrium

Period of a pendulum:

Example 2: Find the period of a pendulum with a 2.45kg bob and having a length of 1.36m. By what would you have to increase the length in order to double the period?

Try it : What is the frequency of a pendulum of length 0.75m that is setup on the surface of Mars where the acceleration due to gravity is about 1/3 of that on Earth? Page 608 Questions 1-4 Page 614 Questions 5-8 (Answer:0.33hz)