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A particle executes SHM with a time peri...

A particle executes SHM with a time period of 2s and amplitude 10 cm . Find its (i) Displacement (ii) Velocity (iii) Acceleration after 1/6 s, Starting from mean position.

Text Solution

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(i)T=2s,A=10 cm
Displacement ,`x=A"sin"(2pi)/(T)t`
`" "=10"sin"(2pi)/(2)xx(1)/(6)=10"sin"(pi)/(6)=5 cm`
(ii) Velocity , `v=(dx)/(dt)=A(2pi)/(T)"cos"(2pi)/(T)t`
`" "=10xx(2pi)/(2)"cos"(2pi)/(2)xx(1)/(6)`
`" "=10xx3.14 xx(sqrt(3))/(2)=27.16` cm/s
(iii) Acceleration , `a=(dv)/(dt)=(4pi^(2))/(T^(2))A"sin"(2pi)/(T)t`
`" "(4xx(3.14)^(2))/(4)xx10xx"sin"(2pi)/(2)xx(1)/(6)`
`" "=49.3 "cm"//s^(2)`
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