Question
Download Solution PDFHow the Potential energy (E) of a particle executing simple harmonic motion varies according to displacement x from mean position?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- Simple harmonic motion occurs when the restoring force or acceleration is directly proportional to the displacement from equilibrium or mean position.
F α -x
Where F = force and x = the displacement from equilibrium.
- Potential Energy of a body performing SHM:
\(E=\frac{1}{2}mω^2 x^2\)
where m is the mass of the body, ω is the angular frequency, and x is the position with respect to time.
EXPLANATION:
Potential Energy of a particle
\(E=\frac{1}{2}mω^2 x^2\)
So E ∝ x2
The correct answer is option 2.
- The kinetic energy of a particle executing SHM is given by:
\(KE=\frac{1}{2}mv^2=\frac{1}{2}m\omega^2(A^2-x^2)\)
- Total Energy of the particle
Total energy = K.E. + P.E.
\(E=\frac{1}{2}mω^2 A^2\)
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