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Question
Which of the following exhibit simple harmonic motion?
I. A pendulum
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
Which of the following exhibit simple harmonic motion?
I. A pendulum
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
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Solution
The correct option is B II only
Simple harmonic motion is defined as the oscillation of an object about an equilibrium position where the restoring force acting on the object is directly proportional to its displacement from the equilibrium position.
Though we often treat pendulum motion as simple harmonic motion, this is in fact a simplification. The restoring force acting on a pendulum is mgsinθ, where θθ is the angle of displacement from the equilibrium position. The restoring force, then, is directly proportional to sin , θθand not to the pendulum bobs displacement, θθ. At small angles, θθ=sin θθ, so we can approximate the motion of a pendulum as simple harmonic motion, but the truth is more complicated.
The motion of a mass attached to a spring is given by Hookes Law, F = kx . Since the restoring force, F, is directly proportional to the masss displacement, x, a mass on a spring does indeed exhibit simple harmonic motion.
There are two forces acting on a bouncy ball: the constant downward force of mg , and the occasional elastic force that sends the ball back into the air. Neither of these forces is proportional to the balls displacement from any point, so, despite the fact that a bouncy ball oscillates up and down, it does not exhibit simple harmonic motion.
Of the three examples given above, only a mass on a spring exhibits simple harmonic motion, so the correct answer is B.
Simple harmonic motion is defined as the oscillation of an object about an equilibrium position where the restoring force acting on the object is directly proportional to its displacement from the equilibrium position.
Though we often treat pendulum motion as simple harmonic motion, this is in fact a simplification. The restoring force acting on a pendulum is mgsinθ, where θθ is the angle of displacement from the equilibrium position. The restoring force, then, is directly proportional to sin , θθand not to the pendulum bobs displacement, θθ. At small angles, θθ=sin θθ, so we can approximate the motion of a pendulum as simple harmonic motion, but the truth is more complicated.
The motion of a mass attached to a spring is given by Hookes Law, F = kx . Since the restoring force, F, is directly proportional to the masss displacement, x, a mass on a spring does indeed exhibit simple harmonic motion.
There are two forces acting on a bouncy ball: the constant downward force of mg , and the occasional elastic force that sends the ball back into the air. Neither of these forces is proportional to the balls displacement from any point, so, despite the fact that a bouncy ball oscillates up and down, it does not exhibit simple harmonic motion.
Of the three examples given above, only a mass on a spring exhibits simple harmonic motion, so the correct answer is B.
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