The total energy of a block, executing simple harmonic motion is:
Correct answer: C. Proportional to 'x2'
- A. Independent of 'x'
- B. Proportional to 'x'
- C. Proportional to 'x2'
- D. Proportional to 'x-2'
- E. Proportional to '√x'
Explanation
The explanation is given below:.The total energy of a block executing simple harmonic motion is the sum of its kinetic energy and potential energy. At any position, the potential energy is proportional to the square of the displacement from the equilibrium position. Therefore, the total energy will also be proportional to the square of the displacement from the equilibrium position.The equation for the total energy of a block executing SHM is:E = 1/2 kx2Where E is the total energy, k is the spring constant, and x is the displacement from the equilibrium position. As we can see, the total energy is proportional to the square of the displacement from the equilibrium position, which is option C.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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