Peoples Physics Book Version-3

10.1. The Big Idea http://www.ck12.org

• 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.


• The kinetic energy and the speed are at a maximum at the equilibrium point, but the potential energy and
  restorative force is zero there.


• At theend pointsthe potential energy is at a maximum, while the kinetic energy and speed are zero. However
  at the end points the restorative force and acceleration are at a maximum.

MEDIA

Click image to the left for more content.

• In SHM since energy is conserved, often, the most fruitful method of calculating position and velocity is to
  set the total energy equal to the sum of kinetic and potential energies. Similarly force and acceleration are best
  calculated by using∑F=ma.

Key Equations and Definitions

Period Equations















T=^1 f Period is the inverse of frequency

Tspring= 2 π

√

m

k

Period of mass mon a spring with constant k

Tpendulum= 2 π

√

L

g

Period of a pendulum of length L

Kinematics of SHM

{

x(t) =x 0 +Acos 2πf(t−t 0 ) Position of an object in SHM of Amplitude A

v(t) =− 2 πf Asin 2πf(t−t 0 ) Velocity of an object in SHM of Amplitude A

Investigation

1. Your task: Match the period of the circular motion system with that of the spring system. You are only allowed
   to change the velocity involved in the circular motion system. Consider the effective distance between the
   block and the pivot to be to be fixed at 1m. The spring constant(13.5N/m) is also fixed. You should view the
   charts to check whether you have succeeded. Instructions: To alter the velocity, simply click on the Select
   Tool, and select the pivot. The Data tab below will allow you to numerically adjust the rotational speed using
   the Motor field. To view the graphs of their respective motion in order to determine if they are in sync, click
   on Chart tab below.