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Calculate the amplitude, angular frequen...

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)`

Text Solution

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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
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