During one complete oscillation of a particle, The average speed is 2 cm/sec. then the maximum velocity is ____ cm/sec
Question
During one complete oscillation of a particle, the average speed is 2 cm/sec. Then the maximum velocity is ____ cm/sec.
Solution
The question is about simple harmonic motion (SHM). In SHM, the maximum velocity (Vmax) is given by the formula:
Vmax = 2πνA
where ν is the frequency of oscillation and A is the amplitude.
The average speed during one complete oscillation in SHM is given by the formula:
Average speed = 2A/T
where T is the time period of oscillation.
Given that the average speed is 2 cm/sec, we can equate the two formulas to solve for Vmax:
2A/T = 2 cm/sec
From this, we can solve for A:
A = T cm
Substituting A into the formula for Vmax gives:
Vmax = 2πνT
However, the frequency ν is the reciprocal of the time period T, so we can substitute ν = 1/T to get:
Vmax = 2π(T/T)
This simplifies to:
Vmax = 2π cm/sec
So, the maximum velocity is 2π cm/sec.
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