What will be the percentage increase in the time period of a simple pendulum when its effective length is increased by 22?

This simple pendulum calculator is a tool that will let you calculate the period and frequency of any pendulum in no time. Read on to learn the period of a pendulum equation and use it to solve all of your pendulum swing problems.

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First of all, a simple pendulum is defined to be a point mass or bob (taking up no space) that is suspended from a weightless string or rod. Such a pendulum moves in a harmonic motion - the oscillations repeat regularly, and kinetic energy is transformed into potential energy, and vice versa.

If you want to calculate the energy of the pendulum, make sure to use our kinetic energy calculator and potential energy calculator.

Surprisingly, for small amplitudes (small angular displacement from the equilibrium position), the pendulum period doesn't depend either on its mass or on the amplitude. It is usually assumed that "small angular displacement" means all angles between -15º and 15º. The formula for the pendulum period is

where:

• T is the period of oscillations - time that it takes for the pendulum to complete one full back-and-forth movement;
• L is the length of the pendulum (of the string from which the mass is suspended); and
• g is the acceleration of gravity. On Earth, this value is equal to 9.80665 m/s² - this is the default value in the simple pendulum calculator.

You can find the frequency of the pendulum as the reciprocal of period:

1. Determine the length of the pendulum. For example, it can be equal to 2 m.
2. Decide a value for the acceleration of gravity. We will use the Earthly figure of 9.80665 m/s², but feel free to check how the pendulum would behave on other planets.
3. Calculate the period of oscillations according to the formula above: T = 2π√(L/g) = 2π * √(2/9.80665) = 2.837 s.
4. Find the frequency as the reciprocal of the period: f = 1/T = 0.352 Hz.
5. You can also let this simple pendulum calculator perform all calculations for you!

For a pendulum with angular displacement higher than 15º, the period also depends on the moment of inertia of the suspended mass. Then, the period of a pendulum equation has the form of:

where:

• m is the mass of the pendulum;
• I is the moment of inertia of the mass; and
• D is the distance from the center of mass to the point of suspension.

To calculate the time period of a simple pendulum, follow the given instructions:

1. Determine the length L of the pendulum.

2. Divide L by the acceleration due to gravity, i.e., g = 9.8 m/s².

3. Take the square root of the value from Step 2 and multiply it by 2π.

4. Congratulations! You have calculated the time period of a simple pendulum.

To determine the acceleration due to gravity using a simple pendulum, proceed as follows:

1. Measure the time period T for one oscillation using a stopwatch.

2. Determine the length L of the pendulum.

3. Divide the length L by the square of the time period T.

4. Multiply the value obtained from Step 3 by 4π² and you will get the value for acceleration due to gravity, g.

To calculate the length of a simple pendulum, use the formula L = (T/ 2π)²*g. Where T is the time period of the simple pendulum and g is the acceleration due to gravity.

99.36 cm. Using the formula, L = (T/ 2π)²*g, we can determine that the length of a simple pendulum with a time period of 2 seconds is 99.36 cm.

Text Solution

Solution : Given, increase in length of the pendulum = 0.21L, where L is the initial length. <br> Hence, increased length L. = L + 0.21 L = 1.21 L <br> Let, the time period change to T. from T due to the change in length. <br> As `TpropsqrtL`, <br> `T/sqrtL` = constant <br> Thus, `T/sqrtL=(T.)/(sqrt(L.))or,T.=sqrt((L.)/L)T=sqrt((1.12L)/L)T=1.1T` <br> `therefore` Increase in time period = `T.-T=1.1T-T` <br> = 0.1 T = 10% of T <br> Hence, the time period increase by 10 %.