InterviewSolution
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InterviewSolution
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A body oscillates with SHM, accroding to the equation, `x=(5.0m)cos[(2pirads^(-1))t+pi//4]` At `t=1.5s`, calculate the `(a)` diplacement `(b)` speed and `(c)` acceleration of the body. |
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Answer» The angular frequency `omega` of the body `= 2pis^(-1)` and its time period `T = 1s` At `t=1.5s` (a) displacement `= (5.0 m) cos [(2 pi s^(-1))xx1.5 s +pi//4]` `=(5.0 m) cos [(3pi + pi//4)]` `= -5.0 xx 0.707 m` `=-2.535` m (b) Using Eq. (14.9), the speed of the body `= -(5.0 m)(2pi s^(-1))sin [(2pi s^(-1))xx1.5 s + pi//4]` `=-(5.0 m)(2pi s^(-1))sin [(3pi +pi//4)]` `=10 pi xx 0.707 ms^(-1)` `=22 ms^(-1)` (c) Using Eq. (14.10), the acceleration of the body `= (2pi s^(-1))^(2) xx` displacement `= -(2pi s^(-1))^(2) xx (-3.535m)` `= 140 ms^(-2)`. |
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