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An object of mass 0.2 kg executes simple...

An object of mass 0.2 kg executes simple harmonic oscillation along the x-axis with a frequency `(25)/pi`. At the position x = 0.04m, the object has kinetic energy 0.5J and potential energy 0.4J. amplitude of oscillation is (potential energy is zero mean position).

Text Solution

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`omega=2pif=sqrt(k/m)" ":. k=(2pif)^(2)m`
Total energy of oscillaion is `(0.5+0.4)=0.9J`
`:.0.9=1/2kA^(2)` or `A=sqrt(1.8/k)=sqrt(1.8/((2pif)^(2)m))`
`=1/(2pif)sqrt((1.8)/0.2)=1/(2pi(25/(pi)))sqrt(1.8/0.2)=3/50 m=6` cm
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