Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below: (a) y=0.3sin(40pit+1.1) (b) y=2cos(pit) (c ) y=3sin(2pit-1.5)

Calculate the amplitude, angular frequency, frequency, time period and

1.	Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below: (a) y=0.3sin(40pit+1.1) (b) y=2cos(pit) (c ) y=3sin(2pit-1.5)
Answer» Solution :Simple harmonic oscillation EQUATION is `y=Asin(omegat+phi_(0))ory=Acos(omegat+phi_(0))` (a) For the wave, `y=0.3sin(40pit+1.1)` Amplitude is `A=0.3` unit Angular frequency `omega=40pi` rad `s^(-1)` Frequency `f=(omega)/(2pi)=(40pi)/(2pi)=20Hz` Time period `T=(1)/(f)=(1)/(20)=0.05s` Initial phase is `phi_(0)=1.1` rad (b) For the wave, `y=2cos(pit)` Amplitude is `A=2` unit Angular frequency `omega=PI` rad `s^(-1)` Frequency `f=(omega)/(2pi)=(pi)/(2pi)=0.5Hz` Time period `T=(1)/(f)=(1)/(0.5)=2s` Initial phase is `phi_(0)=0` rad (C ) For the wave, `y=3sin(2pit+1.5)` Amplitude is `A=3` unit Angular frequency `omega=2pi` rad `s^(-1)` Frequency `f=(omega)/(2pi)=(2pi)/(2pi)=1Hz` Time period `T=(1)/(f)=(1)/(1)=1S` Initial phase is `phi_(0)=1.5` rad