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A particle executed SHM iwht a time period of 3s and amplitude 6cm. Find (i) displacement (ii) velocity and (iii) acceleration, after `1//2` second, starting from the mean position. |
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Answer» Here `T=3s, A=6cm,t=1//2s` (i) As particle is starting from mean position, the displacement of particle at time t is given by `x=Asinomegat=Asin((2pi)/(T))t=6sin((2pi)/(3))xx(1)/(2)` `=6sin((pi)/(2))=6xx(sqrt(3))/(2)=5.196cm ` (ii) Velocity, `v=(dx)/(dt)=(2piA)/(T)cos((2pit)/(T))` `=(2pi)/(3)xx6cos((2pi)/(3))xx(1)/(2)` `=4picos((pi)/(3))=(4pixx1)/(2)=2xx(22)/(7)=6.28cm//s` (iii) Acceleration, `A=(dv)/(dt)=(4pi^(2))/(T^(2))Asin((2pit)/(T))` `=-(4pi^(2)xx6)/(3^(2))sin((2pi)/(3))xx(1)/(2)` `=-(8pi^(2))/(3)sin((pi)/(3))=-(8pi^(2))/(3)xx(sqrt(3))/(2)=-22.8cm^(-2)` In magnitude, `A=22.8cm^(2)`, Here `-ve` sign indicates that acceleration is directed towards mean position whereas displacement is directed away from mean position. |
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