To make the frequency double of a spring oscillation, we have to:
Correct answer: A. Reduce the mass to one fourth
- A. Reduce the mass to one fourth
- B. Quadruple the mass
- C. Double the mass
- D. Half the mass
Explanation
The frequency of a spring oscillation is given by the formula:f = 1 / (2π) √(k/m)Where f is the frequency, k is the spring constant, and m is the mass of the object. To double the frequency, we need f' = 2f. From the formula, f' / f = √(m/m'). Setting f' = 2f gives 2 = √(m/m'), leading to m' = m/4. This means reducing the mass to one-fourth doubles the frequency.Option A is correct because it matches this result. Options B, C, and D are incorrect as they either increase the mass (lowering the frequency) or do not change it to the required extent to double the frequency.
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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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