An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of (25/π) Hz. At the position x = 0.04 m

Question

An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(\mathrm{x}\) axis with frequency of \(\left(\frac{25}{\pi}\right)\) Hz. At the position \(x=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) and potential energy \(0.4 \mathrm{~J}\). The amplitude of oscillation is ........... cm 

Answer 1

Correct answer is :  6 

Total energy = K.E. + P.E.

at \(\mathrm{x}=0.04 \mathrm{~m}, \text{T.E.} =0.5+0.4=0.9 \mathrm{~J}\)

\(\mathrm{T} . \mathrm{E}=1 \mathrm{~m}\omega ^{2} \mathrm{A}^{2}=0.9\)

\( =\frac{1}{2} \times 0.2\left(2 \pi \times \frac{25}{\pi}\right)^{2} \times \mathrm{A}^{2}=0.9 \)

\(\Rightarrow \mathrm{A}=0.06 \mathrm{~m}\)

\(\mathrm{A}=6 \mathrm{~cm}\)