A point particle of mass 0.1 kg is executing SHM with amplitude of 0.1 m. When the particle passes through the mean position, its K. E. is 8 × 10⁻³J. Obtain the equation of motion of this particle if the initial phase of oscillation is 45°.
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Question

A point particle of mass 0.1 kg is executing SHM with amplitude of 0.1 m. When the particle passes through the mean position, its K. E. is 8 × 10⁻³J. Obtain the equation of motion of this particle if the initial phase of oscillation is 45°.

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G1 Physics · Accepted Answer

At the mean position all energy is kinetic: 8×10⁻³=(1/2)(0.1)ω²(0.1)². Hence ω=4 rad s⁻¹. With initial phase 45°=π/4, x=0.1 sin(4t+π/4) m. Correct answer: A.

A point particle of mass 0.1 kg is executing SHM with amplitude of 0.1 m. When the particle passes through the mean position, its K.E. is 8 × 10⁻³J. Obtain the equation of motion of this particle if the initial phase of oscillation is 45°.