A body executes SHM such that its velocity at the mean position is 1m/s andacceleration at one of the extremity is 1.57m/s2. Calculate time period ofvibration
Question
A body executes SHM such that its velocity at the mean position is 1m/s andacceleration at one of the extremity is 1.57m/s2. Calculate time period ofvibration
Solution
The time period of vibration for a body executing Simple Harmonic Motion (SHM) can be calculated using the formula:
T = 2π √(a/v)
where:
- T is the time period,
- a is the acceleration at one of the extremities, and
- v is the velocity at the mean position.
Given that a = 1.57 m/s² and v = 1 m/s, we can substitute these values into the formula:
T = 2π √(1.57/1) T = 2π √1.57 T = 2π * 1.25 T = 2.5π seconds
Therefore, the time period of vibration is approximately 2.5π seconds.
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