the time period is inversely proportional to the heart beat, then f = s One minute is second, ( second = minute ⇒ s − = min − ) f = . s − ⇒ f = . × min − = beats per minute EXAMPLE . Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below a.
y = . sin (40πt + . ) b. y = cos (πt) c.
y = sin (2πt − . ) Solution Simple harmonic oscillation equation is y = A sin(ω t + φ ) or y = A cos(ω t + φ ) a. For the wave, y = . sin(40π t + .
) Amplitude is A = . unit Angular frequency ω = 40π rad s − Frequency f Hz ω π π π Time period T s Initial phase is φ = . rad b. For the wave, y = cos (π t ) Amplitude is A = unit Angular frequency ω = π rad s − Frequency f Hz ω π π π .
Time period T s Initial phase is φ = rad c. For the wave, y = sin(2πt + . ) Amplitude is A = unit Angular frequency ω = 2π rad s − Frequency f Hz ω π π π Time period T s Initial phase is φ = . rad EXAMPLE .
Show that for a simple harmonic motion, the phase difference between a. displacement and velocity is π radian or °. b. velocity and acceleration is π radian or °.
- - - - Unit Oscillations c. displacement and acceleration is π radian or °. Solution a. The displacement of the particle executing simple harmonic motion y = A sinω t Velocity of the particle is t t ω ω ω ω π cos sin The phase