Periodic Time of SHM for Compound Pendulum given Radius of Gyration Calculator

✖The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration [k_G]			+10% -10%
✖Distance of pt of suspension of pendulum from cg is measured length between that point and center of gravity of the body.ⓘ Distance of pt of suspension of pendulum from cg [h]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%

✖Periodic time for compound pendulum is the time taken by a complete cycle of the wave to pass a point.ⓘ Periodic Time of SHM for Compound Pendulum given Radius of Gyration [t_{p pendulum}]

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Periodic Time of SHM for Compound Pendulum given Radius of Gyration

Formula

`"t"_{"p pendulum"} = 2*pi*sqrt(("k"_{"G"}^2+"h"^2)/("g"*"h"))`

Example

`"0.624644s"=2*pi*sqrt((("48mm")^2+("42mm")^2)/("9.8m/s²"*"42mm"))`

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Periodic Time of SHM for Compound Pendulum given Radius of Gyration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Periodic time for compound pendulum = 2*pi*sqrt((Radius of Gyration^2+Distance of pt of suspension of pendulum from cg^2)/(Acceleration due to Gravity*Distance of pt of suspension of pendulum from cg))
t_{p pendulum} = 2*pi*sqrt((k_G^2+h^2)/(g*h))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Periodic time for compound pendulum - (Measured in Second) - Periodic time for compound pendulum is the time taken by a complete cycle of the wave to pass a point.
Radius of Gyration - (Measured in Meter) - The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.
Distance of pt of suspension of pendulum from cg - (Measured in Meter) - Distance of pt of suspension of pendulum from cg is measured length between that point and center of gravity of the body.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration: 48 Millimeter --> 0.048 Meter (Check conversion here)
Distance of pt of suspension of pendulum from cg: 42 Millimeter --> 0.042 Meter (Check conversion here)
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_{p pendulum} = 2*pi*sqrt((k_G^2+h^2)/(g*h)) --> 2*pi*sqrt((0.048^2+0.042^2)/(9.8*0.042))

Evaluating ... ...

t_{p pendulum} = 0.624644121838072

STEP 3: Convert Result to Output's Unit

0.624644121838072 Second --> No Conversion Required

FINAL ANSWER

0.624644121838072 ≈ 0.624644 Second <-- Periodic time for compound pendulum

(Calculation completed in 00.020 seconds)

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Periodic Time of SHM for Compound Pendulum given Radius of Gyration

Go Periodic time for compound pendulum = 2*pi*sqrt((Radius of Gyration^2+Distance of pt of suspension of pendulum from cg^2)/(Acceleration due to Gravity*Distance of pt of suspension of pendulum from cg))

Minimum Periodic Time of SHM for Compound Pendulum

Go Time Period SHM = 2*pi*sqrt(2*Radius of Gyration/Acceleration due to Gravity)

Frequency of Compound Pendulum in SHM

Go Frequency = 1/Periodic time for compound pendulum

Periodic Time of SHM for Compound Pendulum given Radius of Gyration Formula

What is the meaning of time period or periodic time?

The time period is the time taken by a complete cycle of the wave to pass a point, Frequency is the number of the complete cycles of waves passing a point in unit time. Angular frequency is the angular displacement of any element of the wave per unit time.

How to Calculate Periodic Time of SHM for Compound Pendulum given Radius of Gyration?

Periodic Time of SHM for Compound Pendulum given Radius of Gyration calculator uses Periodic time for compound pendulum = 2*pi*sqrt((Radius of Gyration^2+Distance of pt of suspension of pendulum from cg^2)/(Acceleration due to Gravity*Distance of pt of suspension of pendulum from cg)) to calculate the Periodic time for compound pendulum, Periodic Time of SHM for Compound Pendulum given Radius of Gyration is the time taken for one complete cycle of vibration to pass a given point. Periodic time for compound pendulum is denoted by t_{p pendulum} symbol.

How to calculate Periodic Time of SHM for Compound Pendulum given Radius of Gyration using this online calculator? To use this online calculator for Periodic Time of SHM for Compound Pendulum given Radius of Gyration, enter Radius of Gyration (k_G), Distance of pt of suspension of pendulum from cg (h) & Acceleration due to Gravity (g) and hit the calculate button. Here is how the Periodic Time of SHM for Compound Pendulum given Radius of Gyration calculation can be explained with given input values -> 0.624644 = 2*pi*sqrt((0.048^2+0.042^2)/(9.8*0.042)).

FAQ

What is Periodic Time of SHM for Compound Pendulum given Radius of Gyration?

Periodic Time of SHM for Compound Pendulum given Radius of Gyration is the time taken for one complete cycle of vibration to pass a given point and is represented as t_{p pendulum} = 2*pi*sqrt((k_G^2+h^2)/(g*h)) or Periodic time for compound pendulum = 2*pi*sqrt((Radius of Gyration^2+Distance of pt of suspension of pendulum from cg^2)/(Acceleration due to Gravity*Distance of pt of suspension of pendulum from cg)). The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass, Distance of pt of suspension of pendulum from cg is measured length between that point and center of gravity of the body & Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

How to calculate Periodic Time of SHM for Compound Pendulum given Radius of Gyration?

Periodic Time of SHM for Compound Pendulum given Radius of Gyration is the time taken for one complete cycle of vibration to pass a given point is calculated using Periodic time for compound pendulum = 2*pi*sqrt((Radius of Gyration^2+Distance of pt of suspension of pendulum from cg^2)/(Acceleration due to Gravity*Distance of pt of suspension of pendulum from cg)). To calculate Periodic Time of SHM for Compound Pendulum given Radius of Gyration, you need Radius of Gyration (k_G), Distance of pt of suspension of pendulum from cg (h) & Acceleration due to Gravity (g). With our tool, you need to enter the respective value for Radius of Gyration, Distance of pt of suspension of pendulum from cg & Acceleration due to Gravity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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