Peoples Physics Concepts

10.2. Springs http://www.ck12.org

10.2 Springs

• Calculate periods, frequencies, etc. of spring systems in harmonic motion.

Students will learn to calculate periods, frequencies, etc. of spring systems in harmonic motion.

Key Equations

T=^1 f; Period is the inverse of frequency

Tspring= 2 π

√

m

k

; Period of mass m on a spring with constant k

Fs p=−kx; the force of a spring equals the spring constant multiplied by the amount the spring is stretched or

compressed from its equilibrium point. The negative sign indicates it is a restoring force (i.e. direction of the force

is opposite its displacement from equilibrium position.

Us p=^12 kx^2 ; the potential energy of a spring is equal to one half times the spring constant times the distance

squared that it is stretched or compressed from equilibrium

Guidance

• The oscillating object does not lose any energy in SHM. Friction is assumed to be zero.


• In harmonic motion there is always arestorative force,which attempts torestorethe oscillating object to its
  equilibrium position. The restorative force changes during an oscillation and depends on the position of the
  object. In a spring the force is given by Hooke’s Law:F=−kx


• The period,T, is the amount of time needed for the harmonic motion to repeat itself, or for the object to go one
  full cycle. In SHM,Tis the time it takes the object to return to its exact starting point and starting direction.


• The frequency,f,is the number of cycles an object goes through in 1 second. Frequency is measured in Hertz
  (Hz). 1Hz=1 cycle per sec.


• The amplitude,A, is the distance from theequilibrium(or center)pointof motion to either its lowest or highest
  point (end points). The amplitude, therefore, is half of the total distance covered by the oscillating object. The
  amplitude can vary in harmonic motion, but is constant in SHM.

Example 1

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/1836