Time Period for Vibrations Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness)
tp = 2*pi*sqrt(Idisc/q)
This formula uses 1 Constants, 1 Functions, 3 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
Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.
Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
Torsional Stiffness - (Measured in Newton per Meter) - torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.
STEP 1: Convert Input(s) to Base Unit
Mass Moment of Inertia of Disc: 6.2 Kilogram Square Meter --> 6.2 Kilogram Square Meter No Conversion Required
Torsional Stiffness: 5.4 Newton per Meter --> 5.4 Newton per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tp = 2*pi*sqrt(Idisc/q) --> 2*pi*sqrt(6.2/5.4)
Evaluating ... ...
tp = 6.73253830767135
STEP 3: Convert Result to Output's Unit
6.73253830767135 Second --> No Conversion Required
FINAL ANSWER
6.73253830767135 6.732538 Second <-- Time Period
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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13 Natural Frequency of Free Torsional Vibrations Calculators

Natural Frequency of Vibration
Go Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi)
Time Period for Vibrations
Go Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness)
Angular Velocity of Shaft
Go Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc)
Torsional Stiffness of Shaft given Time Period of Vibration
Go Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2
Moment of Inertia of Disc given Time Period of Vibration
Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)
Moment of Inertia of Disc using Natural Frequency of Vibration
Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Frequency)^2)
Torsional Stiffness of Shaft given Natural Frequency of Vibration
Go Torsional Stiffness = (2*pi*Frequency)^2*Mass Moment of Inertia of Disc
Moment of Inertia of Disc given Angular Velocity
Go Mass Moment of Inertia of Disc = Torsional Stiffness of Shaft/(Angular Velocity^2)
Torsional Stiffness of Shaft given Angular Velocity
Go Torsional Stiffness of Shaft = Angular Velocity^2*Mass Moment of Inertia of Disc
Angular Displacement of Shaft from Mean Position
Go Angular Displacement of Shaft = Restoring Force/Torsional Stiffness
Restoring Force for Free Torsional Vibrations
Go Restoring Force = Torsional Stiffness*Angular Displacement of Shaft
Torsional Stiffness of Shaft
Go Torsional Stiffness = Restoring Force/Angular Displacement of Shaft
Accelerating Force
Go Force = Mass Moment of Inertia of Disc*Angular Acceleration

Time Period for Vibrations Formula

Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness)
tp = 2*pi*sqrt(Idisc/q)

What causes torsional vibration?

Torsional vibrations are an example of machinery vibrations and are caused by the superposition of angular oscillations along the whole propulsion shaft system including propeller shaft, engine crankshaft, engine, gearbox, flexible coupling and along the intermediate shafts.

How to Calculate Time Period for Vibrations?

Time Period for Vibrations calculator uses Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness) to calculate the Time Period, The Time Period for Vibrations formula is defined as the time taken by a complete cycle of the wave to pass a point. Time Period is denoted by tp symbol.

How to calculate Time Period for Vibrations using this online calculator? To use this online calculator for Time Period for Vibrations, enter Mass Moment of Inertia of Disc (Idisc) & Torsional Stiffness (q) and hit the calculate button. Here is how the Time Period for Vibrations calculation can be explained with given input values -> 0.54077 = 2*pi*sqrt(6.2/5.4).

FAQ

What is Time Period for Vibrations?
The Time Period for Vibrations formula is defined as the time taken by a complete cycle of the wave to pass a point and is represented as tp = 2*pi*sqrt(Idisc/q) or Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness). Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis & torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.
How to calculate Time Period for Vibrations?
The Time Period for Vibrations formula is defined as the time taken by a complete cycle of the wave to pass a point is calculated using Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness). To calculate Time Period for Vibrations, you need Mass Moment of Inertia of Disc (Idisc) & Torsional Stiffness (q). With our tool, you need to enter the respective value for Mass Moment of Inertia of Disc & Torsional Stiffness 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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