For a simple harmonic motion the acceleration of the body is _ to displacement and always directed towards _.
Correct answer: C. Directly proportional ; mean position
- A. Directly proportional ; maximum position
- B. Inversely proportional ; maximum position
- C. Directly proportional ; mean position
- D. Directly proportional ; minimum position
Explanation
For a simple harmonic motion, the acceleration of the body is directly proportional to the displacement and always directed towards the equilibrium position.In simple harmonic motion, the acceleration of the body is given by the equation:a = -ω²xwhere:a is the acceleration,x is the displacement from the equilibrium position, andω is the angular frequency of the motion.The negative sign indicates that the acceleration is directed towards the equilibrium position. This means that when the body is displaced from its equilibrium position, it experiences an acceleration that acts in the opposite direction, pulling it back towards the equilibrium. As the body moves towards the equilibrium position, the acceleration decreases until it reaches zero at the equilibrium point. Then, as the body moves away from the equilibrium in the opposite direction, the acceleration reverses its direction and continues to oscillate back and forth.The two conditions that have to be met for an oscillatory motion to be simple harmonic are:1- The acceleration is directly proportional to displacement.2- The displacement is always directed opposite to the direction of acceleration, i.e towards the mean position.
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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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