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The periodic time of a particle with simple harmonic motion is __________ proportional to the angular velocity.
- a)directly
- b)inversely
Correct answer is option 'B'. Can you explain this answer?
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The periodic time of a particle with simple harmonic motion is _______...
B) The periodic time of a particle moving with simple harmonic motion is directly proportional to its angular velocity. c) The velocity of a particle moving with simple harmonic motion is zero at the mean position. d) The acceleration of the particle moving with simple harmonic motion is maximum at the mean position.
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The periodic time of a particle with simple harmonic motion is _______...
Explanation:
The periodic time of a particle with simple harmonic motion is the time taken by it to complete one full cycle of oscillation. Angular velocity is the rate of change of angle with respect to time. The relation between the angular velocity and periodic time for simple harmonic motion is given by:
T = (2π/ω)
where,
T = periodic time
ω = angular velocity
Now, let's understand the relation between periodic time and angular velocity:
Therefore, we can conclude that the periodic time of a particle with simple harmonic motion is inversely proportional to the angular velocity.
The periodic time of a particle with simple harmonic motion is the time taken by it to complete one full cycle of oscillation. Angular velocity is the rate of change of angle with respect to time. The relation between the angular velocity and periodic time for simple harmonic motion is given by:
T = (2π/ω)
where,
T = periodic time
ω = angular velocity
Now, let's understand the relation between periodic time and angular velocity:
- Inversely proportional: From the above relation, we can see that the periodic time is inversely proportional to the angular velocity. This means that if the angular velocity increases, the periodic time decreases and vice versa.
- Mathematical explanation: The angular velocity is given by the formula ω = 2π/T. If we substitute this value of ω in the above equation, we get T = (2π/ω). Thus, we can see that T is inversely proportional to ω.
- Physical explanation: When the angular velocity of a particle increases, it means that the particle is oscillating faster. This implies that it takes less time for the particle to complete one full cycle of oscillation. Hence, the periodic time decreases. Similarly, if the angular velocity decreases, the particle oscillates slower and takes more time to complete one full cycle of oscillation, resulting in an increase in the periodic time.
Therefore, we can conclude that the periodic time of a particle with simple harmonic motion is inversely proportional to the angular velocity.
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The periodic time of a particle with simple harmonic motion is __________ proportional to the angular velocity.a)directlyb)inverselyCorrect answer is option 'B'. Can you explain this answer?
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