the speed of pendulum is under root 0.91 and time period 1.8 sec what will be its time period in initial frame of reference
To determine the time period of a pendulum in a different reference frame, we need to consider the concept of time dilation. Time dilation is the phenomenon in which time appears to run slower or faster depending on the relative motion between two observers.
In this case, we need to find the time dilation factor. Let's denote it as "γ" (gamma). The time dilation factor is given by:
γ = 1 / √(1 - v^2 / c^2)
where "v" is the velocity of the pendulum and "c" is the speed of light (a constant).
The speed of the pendulum, in this case, is given as √0.91. So, v = √0.91.
Now, to calculate the time dilation factor γ, we need to know the speed of the pendulum relative to the speed of light. Since the speed of light is much larger than the speed of a pendulum, we can consider the pendulum's speed to be negligible in comparison.
Thus, v << c. This means that the value of v^2 / c^2 will be extremely small, approaching zero. Therefore, we can approximate the value of γ to be approximately 1.
Hence, the time period of the pendulum in the initial frame of reference will effectively remain the same, which is 1.8 seconds.