t ) = A cos + T t For T = s, x ( t ) = A cos + which is a SHM of amplitude A , period s, and an initial phase* = . * The natural unit of angle is radian, defined through the ratio of arc to radius. Angle is a dimensionless quantity. Therefore it is not always necessary to mention the unit ‘radian’ when we use π , its multiples or submultiples.
The conversion between radian and degree is not similar to that between metre and centimetre or mile. If the argument of a trigonometric function is stated without units, it is understood that the unit is radian. On the other hand, if degree is to be used as the unit of angle, then it must be shown explicitly. For example, sin( ) means sine of degree, but sin( ) means sine of radians.
Hereafter, we will often drop ‘rad’ as the unit, and it should be understood that whenever angle is mentioned as a numerical value, without units, it is to be taken as radians. Fig. . In this case at t = , OP makes an angle of o = π with the x -axis.
After a time t , it covers an angle of t in the clockwise sense and makes an angle of π − T t with the x -axis. The projection of OP on the x -axis at time t is given by x ( t ) = B cos π − T t = B sin π T t For T = s, x ( t ) = B sin t Writing this as x ( t ) = B cos t − , and comparing with Eq. ( . ).
We find that this represents a SHM of amplitude B , period s, and an initial phase of − . ⊳ . VELOCITY AND ACCELERATION IN SIMPLE HARMONIC MOTION The speed of a particle