In simple harmonic motion, a particle possesses both kinetic energy and potential energy. The sum of these energies remains constant.
The kinetic energy of a particle in SHM is maximum at the mean position and zero at the extreme positions.
KE = (1/2) m v²
The potential energy of a particle in SHM is maximum at the extreme positions and minimum at the mean position.
PE = (1/2) k x²
where,
k = force constant
x = displacement from mean position
The total mechanical energy of a particle executing SHM is constant and given by:
Total Energy (E) = (1/2) k A²
where,
A = amplitude of oscillation
Q1. In SHM, kinetic energy is maximum at: A) Extreme position B) Mean position C) Halfway D) Everywhere same Answer: B Q2. In SHM, potential energy is maximum at: A) Mean position B) Midway C) Extreme positions D) Everywhere same Answer: C Q3. Formula for potential energy in SHM is: A) (1/2) m v² B) (1/2) k x² C) m g h D) k x Answer: B Q4. Total energy of a particle executing SHM depends on: A) Mass B) Velocity C) Amplitude D) Displacement Answer: C Q5. Total mechanical energy in SHM is: A) Variable B) Zero C) Constant D) Infinite Answer: C Q6. At extreme position, kinetic energy is: A) Maximum B) Minimum C) Zero D) Infinite Answer: C Q7. At mean position, potential energy is: A) Maximum B) Zero C) Minimum D) Infinite Answer: C Q8. Energy in SHM is continuously converted between: A) Heat and sound B) Electrical and magnetic C) Kinetic and potential D) Nuclear and chemical Answer: C
KE = (1/2) m v²
Maximum at mean position.
PE = (1/2) k x²
Maximum at extreme positions.
E = (1/2) k A² (constant)
MCQs and numericals are frequently asked on energy relations and positions in SHM.
