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If x, and a denote the displacement, the velocity and the acceler of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?A. `aT//x`B. `At+2piupsilon`C. `aT//upsilon`D. `a^(2)T^(2)+4pi^(2)upsilon^(2)` |
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Answer» Correct Answer - A `x=rsiniomegat, upsilon=(dx)/(dt)=romegacosomegat,` `a=(dupsilon)/(dt)=-romega^(2)sinomegat =-omega^(2)x.` So, `(aT)/(x)=(-omega^(2)xxxT)/(x)=-omega^(2)T=-(4pi^(2))/(T^(2))xxT` `=-(4pi^(2))/(T)=a ` constant `(aT)/(upsilon)=(-omega^(2)rsinomegat xxT)/(omegar cos omegat )=-omegaTtanomegat` `=(2pi)/(T)xxTtanomegat =(`not constant ) `aT+2piupsilon` is not constant. `a^(2)T^(2)+4pi^(2)upsilon^(2)` is also not constant. |
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