Hz). Mathematically, frequency is related to time period by = ( . ) The number of cycles (or revolutions) per second is called angular frequency. It is usually denoted by the Greek small letter ‘omega’, ω.
Comparing equation ( . ) and equation ( . ), angular frequency and frequency are related by ω = πf ( . ) SI unit for angular frequency is rad s − .
(read it as radian per second) (iii) Phase The phase of a vibrating particle at any instant completely specifies the state of the particle. It expresses the position and direction of motion of the particle at that instant with respect to its mean position (Figure . ). y = A sin (ω t + φ ) ( .
) where ω t + φ = φ is called the phase of the vibrating particle. At time t = s (initial time), the phase φ = φ is called epoch (initial phase) where φ is called the angle of epoch. Phase difference: Consider two particles executing simple harmonic motions. Their - - - - Unit Oscillations equations are y = A sin(ω t + φ ) and y = A sin(ω t + φ ), then the phase difference ∆φ= (ω t + φ ) − (ω t + φ ) = φ −φ .
A sin φ i +A Amplitude x Phase at instant t i : φ ( t i ) = ω t i + φ i Phase at t = : φ i –A t i ω t π ω A sin φ ( t i ) ω π Figure . The phase of vibrating particle at two instant of time. EXAMPLE . A nurse measured the average heart beats of a patient and reported to the doctor in terms of time period as .
s . Express the heart beat of the patient in terms of number of beats measured per minute. Solution Let the number of heart beats measured be f . Since