Question 235: Oscillations

Question

An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$. At the position $x=0.04 \mathrm{~m}$, the object has kinetic energy 1 J and potential energy 0.6 J . The amplitude of oscillation is

Accepted Answer

$$ \begin{aligned} &\begin{aligned} & 	ext { Total energy }=K . E .+P . E .=K+P=\frac{1}{2} m \omega^2 A^2 \ & A^2=\frac{2(K+P)}{m \omega^2} \ & A=\frac{1}{\omega} \sqrt{\frac{2(K+P)}{m}}=\frac{1}{2 \pi n} \sqrt{\frac{2(K+P)}{m}}=\frac{1}{\pi n} \sqrt{\frac{K+P}{2 m}} \end{aligned}\ &	ext { Substituting the values, }\ &A=\frac{1}{\pi} 	imes \frac{\pi}{25} \sqrt{\frac{1+0.6}{2 	imes 0.2}}=0.08 \mathrm{~m} \end{aligned} $$

Answer

0.06 m

Answer

0.6 m

Answer

0.08 m

Answer

0.8 m

Oscillations

An object of mass 0.2 kg executes simple harmonic oscillations along the x -axis with frequency of \left(\frac{25}{\pi}\right) \mathrm{Hz}. At the position x=0.04 \mathrm{~m}, the object has kinetic energy 1 J and potential energy 0.6 J . The amplitude of oscillation is

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