Simple Pendulums: Calculating Time to Attain Greatest Speed

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In summary, the conversation discusses a simple pendulum with a 0.67 m long string and a small ball attached to its free end. The question is how much time elapses before the ball attains its greatest speed after being released from rest. The equations f=frequency and f=1/T are used to solve for the period, with the final answer being T=.166s. However, it is suggested to redo the calculation and divide the period by 4, as reaching the bottom takes one-quarter of the period.
  • #1
alyse!!
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Homework Statement




A simple pendulum is made from a 0.67 m long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?

Homework Equations



f=frequency
f=(1/2pi)(g/L)^.5

f=1/T
where T=period

The Attempt at a Solution




f=1/T

f=(1/2pi)((9.8m/s^2)/0.67m))^.5
f=6.007

f=1/T
6.007=1/T
T=1/6.007
T=.166s

This is the answer that i got but it is wrong and i do not know why, and now how to do it if this is the wrong way.
 
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  • #2
alyse! said:
f=(1/2pi)((9.8m/s^2)/0.67m))^.5
f=6.007
Redo this calculation.
 
  • #3
Redo the calculation, perhaps, and divide period by 4, since reaching the bottom takes one-quarter of the period.
 

What is a simple pendulum?

A simple pendulum is a physical system consisting of a mass suspended from a fixed point by a string or rod. The mass is allowed to swing back and forth under the influence of gravity, creating a periodic motion.

What is the formula for calculating the time to attain greatest speed in a simple pendulum?

The formula for calculating the time to attain greatest speed in a simple pendulum is T = 2π√(l/g), where T is the period (time) of the pendulum, l is the length of the string or rod, and g is the acceleration due to gravity.

How does the length of the string or rod affect the time to attain greatest speed in a simple pendulum?

The length of the string or rod has a direct impact on the period of the pendulum, and therefore, the time to attain greatest speed. A longer length will result in a longer period and a shorter length will result in a shorter period.

How does the mass of the pendulum affect the time to attain greatest speed in a simple pendulum?

The mass of the pendulum does not affect the time to attain greatest speed in a simple pendulum. The period and frequency of a pendulum are only dependent on the length and acceleration due to gravity, not the mass.

Can the time to attain greatest speed be measured experimentally?

Yes, the time to attain greatest speed in a simple pendulum can be measured experimentally by using a stopwatch to time the number of swings in a given time period. This can then be used to calculate the period and the time to attain greatest speed using the formula T = 2π√(l/g).

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