The motion of the pendulum is periodic. This type of motion is characterised by its periodicity with acceleration directed towards a fixed point. The magnitude of its acceleration is proportional to the distance from the fixed point.So, its velocity can also be calculated for any fixed point. The pendulum's acceleration and velocity are variable character.They are not dependent on the mass or material of the bob. We say normally say acceleration and velocity at any point of time , or when the pendulum is at a point on its path of oscillation:
Acceleration = -conxtant times the distance from the fixed point. Alternatively,the rate of change of velocity = -constant times distant from the fixed point.
From the above we can arrive at the velocity of the oscillating pendulum at an instant on ts path:
Velocity = square root of (square of half the amplitude - square od its distance drom the fixed point).
If v is the velocity of the pendulum at any time t and the distance is x from the fixed ( or mid point of the amplitude). then:
v = square root(a^2-x^2), where a is the half amplitude.
By this, we see that the velocity of the pendulum at any point of time is independent of the mass of the pendulum. But the velocity is dependent on the x and a factors. In otherwords, it is depending on the distance from the mid point of the oscillation(or mean point of oscillation) and also on the amplitude of the oscillation. Once again, x and a are dependent on the length of the pendulum but not on the gravitation. Therfore, the velocity is not dependent on mass of the bob, it is dependent on the distance from the mid point and amplitude, but it does not depend on acceleration due to gravity also.
Hope this helps.
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