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Answer :

So, at `pi/120 ` sec it first comes to rest
<br>`t=pi/30sec` <br> `rarr t=pi/30sec`Solution :

`x=5(20t+pi/3)` <br> a. Max displacement from the mean position = Amplitude of the particle. <br> At the extreme position the velocity becomes 0 <br> `:. x=5=Amplitude` <br> `:. 5=5sin(20t+pi/3)` <br> `sin(20t+pi/3)=1=sinpi/2` <br> `rarr 20t+pi/3=pi/2` <br> `rarr t=pi/120sec`e <br> `So, at pi/120 ` sec it first comes to rest <br> `b. a=omega^2x` <br> `=omega^2[5sin(20t+pi/3)]` <br>Fro `a=0,` <br> `5sin(20t+pi/3)=0` <br> `rarr sin(20t+pi/3)=sinx` <br> `rarr 20t=pi-pi/3=(2pi)/3` <br> `t=pi/30sec` <br> c. `v=Aomegacos(omegat+pi/3)` lt. when omega is maximum i.e. `cos(20t+pi/3)=-1=cospi` <br> `20t=pi-pi/3=(2pi)/3` <br> `rarr t=pi/30sec`