What is the relationship between bob mass and frequency?
NO! The mass of the bob does not affect the speed of the pendulum in any way.
Factors affecting the speed of the pendulum:
- Effective legth or the length of the string.
- Acceleration due to gravity at that place.
the string length is the thing that will change the speed of the swing. If the bob has 2 lbs or 200 lbs it will not change the speed of the swing.
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.
Pendulums can be of many different types. A simple pendulum consists of a bob or a weigh hanging at the end of a string or a wire. When the bob of the pendulum is pulled aside and let go it swings back and forth under the influence of gravitational force of the Earth. That is, the pendulum starts oscillating.
The path travelled by the bob while oscillating is called the arc of the pendulum. The travel of bob from one end of the arc to the other and back to the original point is called one oscillation of the pendulum. The time taken for one oscillation is called period of the pendulum. I believe when you are saying the speed of the pendulum, you mean number of oscillation of the pendulum in unit time. Higher the speed of the pendulum, higher the number of oscillation per minute, or lower the period of oscillation.
The period of oscillation of a pendulum is dependent only on two factors - length of the pendulum and the gravitational force of the earth. The period increases with the increase in length, and decreases with increase in gravitational force. The mass of the bob has no effect on speed of the pendulum. Similarly the amplitude of the pendulum - that is the distance between two extreme points of the arc - has no impact on speed of the pendulum.
The gravitational force of the earth at any place remains constant. Therefore at any given place the period of the pendulum is dependent only on length of pendulum. The gravitational force reduces slightly as we move to higher altitudes, and therefore the pendulum of same length will have slightly longer period at higher altitudes.
A 248.7 mm long simple pendulum will have a period of one second at sea level. This period will double if the length is made four times, and triple if length is made nine times.
Does the mass of the bob on a pendulum effect the speed?