A spring system executes simple harmonic motion. If a load is added to it then the time period of the spring-mass system will be:
Correct answer: A. increased
- A. increased
- B. decreased
- C. the same
- D. halved
Explanation
The time period T of a spring-mass system is given by the formula T = 2π√(m/k), where m is the mass and k is the spring constant. As mass m increases, the time period T also increases because it is proportional to the square root of the mass. Therefore, when a load is added, the time period increases. This explains why the correct answer is 'increased'. The other options are incorrect because they do not align with the mathematical relationship between mass and time period in this system.
This question appeared on the ETEA MDCAT 2012 paper, which you can sit online with every answer explained.
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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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