An object of mass 0.2 kg executes simple harmonic oscillations along the X - axis with frequency of ( π 25 ) Hz . At a certain position, the object has kinetic energy 1 J and potential energy 0.6 J

Question

An object of mass 0.2 kg executes simple harmonic oscillations along the X - axis with frequency of ( π 25 ​ ) Hz . At a certain position, the object has kinetic energy 1 J and potential energy 0.6 J . The amplitude of oscillation is

TestHub · Accepted Answer

The total energy of a particle executing simple harmonic motion is the sum of its kinetic and potential energies.

$E = K + U$

$E = 1 + 0.6 = 1.6$ J

The angular frequency of oscillation is given by:

$ω = 2 π f = 2 π (\frac{25}{π}) = 50$ rad/s

The total energy in SHM is also given by the formula:

$E = \frac{1}{2} m ω^{2} A^{2}$

Substituting the given values:

$1.6 = \frac{1}{2} \times 0.2 \times (50)^{2} \times A^{2}$

$1.6 = 0.1 \times 2500 \times A^{2}$

$1.6 = 250 A^{2}$

$A^{2} = \frac{1.6}{250} = \frac{16}{2500}$

$A = \frac{4}{50} = 0.08$ m

Answer: 0.08 m

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