Angular Frequency given Time Period of Motion Calculator

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Free Vibration of Single DOF Undamped Torsional System

✖Time Period SHM is time required for the periodic motion.ⓘ Time Period SHM [t_p]

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✖Angular Frequency in Radian/sec refers to the angular displacement per unit of time.ⓘ Angular Frequency given Time Period of Motion [ω']

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Formula

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Angular Frequency given Time Period of Motion

Formula

`"ω'" = 2*pi/"t"_{"p"}`

Example

`"1.256637rad/s"=2*pi/"5s"`

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Angular Frequency given Time Period of Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Frequency = 2*pi/Time Period SHM
ω' = 2*pi/t_p
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Angular Frequency - (Measured in Radian per Second) - Angular Frequency in Radian/sec refers to the angular displacement per unit of time.
Time Period SHM - (Measured in Second) - Time Period SHM is time required for the periodic motion.

STEP 1: Convert Input(s) to Base Unit

Time Period SHM: 5 Second --> 5 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω' = 2*pi/t_p --> 2*pi/5

Evaluating ... ...

ω' = 1.25663706143592

STEP 3: Convert Result to Output's Unit

1.25663706143592 Radian per Second --> No Conversion Required

FINAL ANSWER

1.25663706143592 ≈ 1.256637 Radian per Second <-- Angular Frequency

(Calculation completed in 00.004 seconds)

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

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National Institute of Technology (NIT), Tiruchirapalli

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< 14 Elements of Vibration Calculators

Velocity of Body in Simple Harmonic Motion

Go Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds)

Magnitude of Acceleration of Body in Simple Harmonic Motion

Go Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds)

Work Done by Harmonic Force

Go Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference)

Displacement of Body in Simple Harmonic Motion

Go Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds)

Frequency given Spring Constant and Mass

Go Vibrational Frequency = 1/(2*pi)*sqrt(Spring Stiffness/Mass Attached to Spring)

Angular Frequency

Go Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring)

Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion

Go Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude

Maximum Velocity of Body in Simple Harmonic Motion

Go Maximum Velocity = Angular Velocity*Vibrational Amplitude

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement

Go Acceleration = Angular Velocity^2*Displacement of Body

Period of Motion in Simple Harmonic Motion

Go Time Period of Oscillations = 2*pi/Angular Velocity

Damping Force

Go Damping Force = Damping Coefficient*Velocity of Body

Inertia Force

Go Inertia Force = Mass Attached to Spring*Acceleration

Spring Force

Go Spring Force = Spring Stiffness*Displacement of Body

Angular Frequency given Time Period of Motion

Go Angular Frequency = 2*pi/Time Period SHM

Angular Frequency given Time Period of Motion Formula

Angular Frequency = 2*pi/Time Period SHM
ω' = 2*pi/t_p

What is angular frequency?

angular frequency is a scalar measure of rotation rate. It refers to the angular displacement per unit time or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument of the sine function.

How to Calculate Angular Frequency given Time Period of Motion?

Angular Frequency given Time Period of Motion calculator uses Angular Frequency = 2*pi/Time Period SHM to calculate the Angular Frequency, Angular Frequency given Time Period of Motion is a measure of how quickly an object completes one full cycle of motion in radians. It represents the rate at which the object oscillates or rotates. The unit of angular frequency is radians per second (rad/s). Angular Frequency is denoted by ω' symbol.

How to calculate Angular Frequency given Time Period of Motion using this online calculator? To use this online calculator for Angular Frequency given Time Period of Motion, enter Time Period SHM (t_p) and hit the calculate button. Here is how the Angular Frequency given Time Period of Motion calculation can be explained with given input values -> 1.256637 = 2*pi/5.

FAQ

What is Angular Frequency given Time Period of Motion?

How to calculate Angular Frequency given Time Period of Motion?

Angular Frequency given Time Period of Motion is a measure of how quickly an object completes one full cycle of motion in radians. It represents the rate at which the object oscillates or rotates. The unit of angular frequency is radians per second (rad/s) is calculated using Angular Frequency = 2*pi/Time Period SHM. To calculate Angular Frequency given Time Period of Motion, you need Time Period SHM (t_p). With our tool, you need to enter the respective value for Time Period SHM and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angular Frequency?

In this formula, Angular Frequency uses Time Period SHM. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring)

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