Why should the angle of oscillation of a simple pendulum be small?

Small Angular Displacements Produce Simple Harmonic Motion The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude.

Why do we use 20 oscillations instead of just one to find the period T?

The uncertainty is given by half of the smallest division of the ruler that we used. In order to minimize the uncertainty in the period, we measured the time for the pendulum to make 20 oscillations, and divided that time by 20.

Why should you calculate the period from 25 oscillations instead of just 1 oscillation?

The more oscillations you measure, the more accurate will be your result for the average oscillation. That’s because when you divide by the number of oscillations to take the average, you also divide your measurement uncertainty by that number. This is true up to a limit.

Why is it important to only have the pendulum swings through an angle of less than 15 degrees?

A pendulum swinging through a large angle is being pulled down by gravity for a longer part of its swing than a pendulum swinging through a small angle, so it speeds up more, covering the larger distance of its big swing in the same amount of time as the pendulum swinging through a small angle covers its shorter …

Why do we use heavy bob which is small in size?

Reason for use This maximizes the moment of inertia, and minimises the length of pendulum required for a given period. Shorter pendulums allow the clock case to be made smaller, and also minimize the pendulum’s air resistance.

Why does a pendulum not depend on mass?

The reason the simple pendulum has no dependence on mass is because the mass gets to “count” for two different things. (The same thing happens in freefall motion, where all things of all weights fall at the same rate.) For a mass-spring system, the mass still affects the inertia, but it does not cause the force.

How many oscillations would you need to be able to measure the gravitational difference?

To measure T, measure the time for 25 or 50 oscillations (swings) and then divide that time by 25 or 50.

What is the purpose of timing 50 oscillations instead of only one to determine the periodic time?

By timing 50 oscillations, you spread that error out across 50 cycles instead of one, causing your measurement to be 50 times more precise. Similar effects are achieved in other types of observations.

Why is it better to measure the period of 10 oscillations rather than the period of one oscillation?

For example, you can measure 10 seconds to +/- 0.1 second, or you can measure 100 seconds to +/- 0.1 second. That error is a smaller fraction of the longer period, so our percent accuracy is better. So they do 10 oscillations to reduce the error in the result by a factor of 10.

Why does pendulum swing slower?

Longer pendulums swing with a lower frequency than shorter pendulums, and thus have a longer period. The momentum built up by the acceleration of gravity causes the mass to swing in the opposite direction to a height equal to the original position.)

Why doesn’t the mass of the pendulum bob affect the period?

The mass of a pendulum’s bob does not affect the period. As mass increases, so does the force on the pendulum, but acceleration remains the same. (It is due to the effect of gravity.) Because acceleration remains the same, so does the time over which the acceleration occurs.

How or why does a pendulum oscillate?

A pendulum is a weight suspended from a pivot so that it can swing freely. When released, the restoring force acting on the pendulum’s mass causes it to oscillate about the equilibrium position, swinging back and forth.

Does the mass of a Bob affect the movement of pendulum?

The movement of the pendula will not differ at all because the mass of the bob has no effect on the motion of a simple pendulum. The pendula are only affected by the period (which is related to the pendulum’s length) and by the acceleration due to gravity.

What is simple pendulum in simple harmonic motion?

A pendulum in simple harmonic motion is called a simple pendulum. A pendulum has an object with a small mass, also known as the pendulum bob, which hangs from a light wire or string. The equilibrium position for a pendulum is where the angle θ is zero (that is, when the pendulum is hanging straight down).

How do you measure the period of an oscillating pendulum?

Cut a piece of a string or dental floss so that it is about 1 m long. Attach a small object of high density to the end of the string (for example, a metal nut or a car key). Starting at an angle of less than 10º, allow the pendulum to swing and measure the pendulum’s period for 10 oscillations using a stopwatch.

What is the equilibrium position of a pendulum?

A pendulum has an object with a small mass, also known as the pendulum bob, which hangs from a light wire or string. The equilibrium position for a pendulum is where the angle θ is zero (that is, when the pendulum is hanging straight down). It makes sense that without any force applied, this is where the pendulum bob would rest.