T=2(pi)sqrt(L/g) T=2(pi)sqrt(.5/9.8)
A simple pendulum with a length of 45m has a period of 13.46 seconds. If the string is weightless, then the mass of the bob has no effect on the period, i.e. it doesn't matter.
A pendulum whose period is precisely two seconds, one second for a swing forward and one second for a swing back, has a length of 0.994 m or 39.1 inches.
The equation is: http://hyperphysics.phy-astr.gsu.edu/HBASE/imgmec/pend.gif T is the period in seconds, L is pendulum length in cm, g is acceleration of gravity in m/s2. We know on earth the period is 1s when the acceleration of gravity is 9.8m/s2, so the pendulum length is 24.824cm. The acceleration of gravity on the moon is 1.6m/s2. Substitute 24.824cm for L and 1.6 for g and you yield 2.475 seconds. The period is 2.475 seconds.
make shorter length
Well compare a pendulum with swing. If the swing length is short, you will quickly return back to your middle position. Similarly in a pendulum if you have a long string, the time take to complete one swing will be more. This means Time period is directly proportional to the increase in length . But by various experiments, they have found that T Is proportional to sq root of length. T = 2pi sq root of (length /g) If you wish to clarify physics doubts, please subscribe to my handle @Raj-bi7xp
5.94 m
Nice problem! I get 32.1 centimeters.
A simple pendulum with a length of 45m has a period of 13.46 seconds. If the string is weightless, then the mass of the bob has no effect on the period, i.e. it doesn't matter.
A pendulum whose period is precisely two seconds, one second for a swing forward and one second for a swing back, has a length of 0.994 m or 39.1 inches.
To predict the period of a pendulum, we can use the equation T = 2Ļā(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity. Plugging in L = 24cm (or 0.24m) and g = 9.8 m/sĀ², we can calculate the period using this equation.
If the length of the second pendulum of the earth is about 1 meter, the length of the second pendulum should be between 0.3 and 0.5 meters.
The equation is: http://hyperphysics.phy-astr.gsu.edu/HBASE/imgmec/pend.gif T is the period in seconds, L is pendulum length in cm, g is acceleration of gravity in m/s2. We know on earth the period is 1s when the acceleration of gravity is 9.8m/s2, so the pendulum length is 24.824cm. The acceleration of gravity on the moon is 1.6m/s2. Substitute 24.824cm for L and 1.6 for g and you yield 2.475 seconds. The period is 2.475 seconds.
make shorter length
Well compare a pendulum with swing. If the swing length is short, you will quickly return back to your middle position. Similarly in a pendulum if you have a long string, the time take to complete one swing will be more. This means Time period is directly proportional to the increase in length . But by various experiments, they have found that T Is proportional to sq root of length. T = 2pi sq root of (length /g) If you wish to clarify physics doubts, please subscribe to my handle @Raj-bi7xp
equation for time in pendulum: t = 2 * pi * ( sq. root (l / g)) key: t = time elapsed ( total, back and forth ) l = length , from pivot to centre of gravity g = acceleration due to gravity say 1 metre length pendulum on earth @ 9.82 (m/s)/s, t = 2.005 seconds same pendulum on neptune @ 11.23 (m/s)/s, t = 1.875 seconds
the period T of a rigid-body compound pendulum for small angles is given byT=2π√I/mgRwhere I is the moment of inertia of the pendulum about the pivot point, m is the mass of the pendulum, and R is the distance between the pivot point and the center of mass of the pendulum.For example, for a pendulum made of a rigid uniform rod of length L pivoted at its end, I = (1/3)mL2. The center of mass is located in the center of the rod, so R = L/2. Substituting these values into the above equation gives T = 2π√2L/3g. This shows that a rigid rod pendulum has the same period as a simple pendulum of 2/3 its length.
Time period and length of a pendulum are related by: T = 2(pi)(L).5(g).5 so putting in the values and solving for g yields a result of : g = 9.70 ms-2