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) F elastic = -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  Pg and 3  Pg and 2  Pg and 2 top of page  Pg and 2 bottom of page