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The period of a simple pendulum is given by the formulaT = 2*pi*sqrt(L/g)
where T = period
L = length
and g = local acceleration due to gravity.
Note that this formula is applicable only when the angular displacement of the pendulum is small. For a displacement of 22.5 degrees (a quarter of a right angle), the true period is approx 1% longer : a clock will lose more than 1/2 a minute every hour!
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How Can a compound pendulum be treated as a simple pendulum?
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.
How does the length of the pendulum effect the pendulum?
The longer the length of the pendulum, the longer the time taken for the pendulum to complete 1 oscillation.
How does the length of a pendulum affect the frequency?
A longer pendulum will have a smaller frequency than a shorter pendulum.
What is the equation for pendulums?
The most accurate way to model a pendulum (without air resistance) is as a differential equation in terms of the angle it makes with the vertical, θ, the length of the pendulum, l, and the acceleration due to gravity, g. d²θ/dt² = -g*sin(θ)/l There is no easy way to integrate this to get θ as a function of time, but if you assume θ is small, you can use the small angle approximation sin(θ)~θ which makes the equation d²θ/dt² = -g*θ/l Which can then be integrated to get the solution θ(t)=θmax*sin(t*√(g/l)) Using this equation, you can easily derive that the period of the pendulum (time required to go through one full cycle) would be T=2π*√(l/g) If air resistance is also accounted for in the original differential equation, the exact equation will be much harder to derive, but in general will involve an exponential decay of a sin function.
Which factor affects the period of the pendulum?
The period of a pendulum is affected by the angle created by the swing of the pendulum, the length of the attachment to the mass, and the weight of the mass on the end of the pendulum.
