SHM and uniform circular motion(DISPLACEMENT)

Displacement

If we count the the time t=0 from the instant when P is passing through O1, the angle which the radius OP sweeps out in time t is angle O1OP= theta= omega.t . The displacement x of N at instant t will be

x =ON = OPsin angle O1OP

x = x _o sin theta

x = x _o sin omega t

This will also be the displacement of the pointer P1 at the instant t.

Phase of vibration

The angle theta gives the states of the system in its vibrational cycle.

Example

at the start of the cycle, theta = 0

halfway through the cycle, theta = 180( pi radians)

when theta = 270, the cycle is three fourth completed

when quarter of the cycle is completed, phase of vibration is 90

frequency

period

amplitude

circular motion:

radius

angular frequency

position of pointer P at t=0

projection of P on diameter DE

f

T

x _o = AB = AC

circular motion

x _o = OP

omega = 2 pi / T

O1

N

radius of the circle is equal to

amplitude of the pointers motion

motion of N is

a replica of the pointers motion