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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.
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.
How does the length of a pendulum affect the frequency?
A longer pendulum will have a smaller frequency than a shorter pendulum.
How do you predict the period of the pendulum if the length of string was 24cm?
The period of a pendulum (for very small swings) can be estimated as ...T = 2 pi (L/G)0.5... so, plugging in 0.024 m for L, and 9.81 m s-2 for G, we get L = 0.31 seconds.
What is the equation for the period of a simple pendulum?
The equation for the period (T) of a simple pendulum is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
What is the physics equation for the period of a pendulum?
The physics equation for the period of a pendulum is T 2(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
What is the derivation of the damped pendulum equation and how does it describe the motion of a pendulum with damping effects?
The damped pendulum equation is derived from Newton's second law of motion and includes a damping term to account for the effects of air resistance or friction on the pendulum's motion. This equation describes how the pendulum's oscillations gradually decrease in amplitude over time due to the damping effects, resulting in a slower and smoother motion compared to an undamped pendulum.
What is the equation for the period of a pendulum and how is it calculated?
The equation for the period of a pendulum is T 2(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. The period is calculated by taking the square root of the ratio of the length of the pendulum to the acceleration due to gravity, and then multiplying by 2.
What is the formula for calculating the amplitude of a pendulum?
The formula for calculating the amplitude of a pendulum is given by the equation: amplitude maximum angle of swing.
What happens to the period o a pendulum when its length is increased?
If the length of a pendulum is increased, the period of the pendulum also increases. This relationship is described by the equation for the period of a pendulum, which is directly proportional to the square root of the length of the pendulum. This means that as the length increases, the period also increases.
What is the solution to the damped pendulum differential equation?
The solution to the damped pendulum differential equation involves using mathematical techniques to find the motion of a pendulum that is affected by damping forces. The solution typically involves finding the general solution using methods such as separation of variables or Laplace transforms, and then applying initial conditions to determine the specific motion of the pendulum.
Why does the mass of pendulum not affect its period?
The period of a pendulum is influenced by the length of the pendulum and the acceleration due to gravity. The mass of the pendulum does not affect the period because the force of gravity acts on the entire pendulum mass, causing it to accelerate at the same rate regardless of its mass. This means that the mass cancels out in the equation for the period of a pendulum.
Why time period of simple pendulum is independent of mass?
The time period of a simple pendulum depends only on the length of the pendulum and the acceleration due to gravity, not the mass of the pendulum bob. This is because the mass cancels out in the equation for the time period, leaving only the factors that affect the motion of the pendulum.
If you want to double the period of a pendulum by how much do you need to change the length?
The period of a pendulum is approximated by the equation T = 2 pi square-root (L / g). Note: This is only an approximation, applicable only for very small angles of swing. At larger angles, a circular error is introduced, but the basic equation still holds true.Looking at that equation, you see that time is proportional to the square root of the length of the pendulum, so to double the period of a pendulum you need to increase its length by a factor of four.
What is the double pendulum equation of motion according to Newton's laws of motion?
The double pendulum equation of motion, according to Newton's laws of motion, is a set of differential equations that describe the motion of a system with two connected pendulums. These equations take into account the forces acting on each pendulum, such as gravity and tension, and how they affect the motion of the system over time.
What does the frequency of a pendulum depend on?
The frequency of a pendulum depends on the length of the pendulum and the acceleration due to gravity. It is described by the equation f = 1 / (2π) * √(g / L), where f is the frequency, g is the acceleration due to gravity, and L is the length of the pendulum.
