Simple Harmonic Motion

Restoring Forces in Spring  F=-kx  This implies that when a spring is compressed or elongated, there is a force that tries to bring it back to its equilibrium position.  Assuming there is not friction (dampening) this will start an oscillation in the spring known as simple harmonic motion.  Max acceleration occurs at maximum displacements and maximum velocity occurs as the spring passes through the equilibrium position.

Amplitude, Frequency, Period  Amplitude – maximum displacement from equilibrium position. Can be measured in meters, degrees, or radians.  Frequency – the number of cycles per second. Units are 1/s or Hertz(Hz)  Period – The amount of time for one complete cycle. Units are s.  Period and frequency are inverses of each other. T = 1/f and f = 1/T

Period of a Spring  The period of SHM in a spring is dependent upon the mass attached to the spring and the magnitude of the spring constant.

Pendulums  A pendulum consists of a bob(mass) attached to a string or rod of a certain length.  When displaced from its equilibrium position, gravity acts as a restoring force creating SHM.  The equation for the period of a pendulum only holds true for small angles ≥ 10 degrees approximately.  Period only depends on the length of the pendulum on Earth.

Energy in SHM  Maximum potential energy occurs at maximum amplitude and can be given as E = 1/2kA 2 At any point along the path the total energy remains constant and should equal the energy at the maximum amplitude. At any location where the object is displaced from equilibrium and moving we can say. E = 1/2kA 2 = 1/2kx 2 + 1/2mv 2