Time Period of Free Longitudinal Vibrations Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)
tp = 2*pi*sqrt(W/sconstrain)
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.
Weight of Body in Newtons - (Measured in Newton) - Weight of Body in Newtons is the force with which a body is pulled toward the earth.
Stiffness of Constraint - (Measured in Newton per Meter) - Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.
STEP 1: Convert Input(s) to Base Unit
Weight of Body in Newtons: 8 Newton --> 8 Newton No Conversion Required
Stiffness of Constraint: 13 Newton per Meter --> 13 Newton per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tp = 2*pi*sqrt(W/sconstrain) --> 2*pi*sqrt(8/13)
Evaluating ... ...
tp = 4.92893607520434
STEP 3: Convert Result to Output's Unit
4.92893607520434 Second --> No Conversion Required
FINAL ANSWER
4.92893607520434 4.928936 Second <-- Time Period
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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12 Equilibrium Method Calculators

Load Attached to Free End of Constraint
Go Weight of Body in Newtons = (Static Deflection*Young's Modulus*Cross Sectional Area)/Length of Constraint
Length of Constraint
Go Length of Constraint = (Static Deflection*Young's Modulus*Cross Sectional Area)/Weight of Body in Newtons
Restoring Force using Weight of Body
Go Force = Weight of Body in Newtons-Stiffness of Constraint*(Static Deflection+Displacement of Body)
Acceleration of Body given Stiffness of Constraint
Go Acceleration of Body = (-Stiffness of Constraint*Displacement of Body)/Load Attached to Free End of Constraint
Displacement of Body given Stiffness of Constraint
Go Displacement of Body = (-Load Attached to Free End of Constraint*Acceleration of Body)/Stiffness of Constraint
Time Period of Free Longitudinal Vibrations
Go Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)
Angular Velocity of Free Longitudinal Vibrations
Go Natural Circular Frequency = sqrt(Stiffness of Constraint/Mass suspended from spring)
Critical Damping Coefficient given Spring Constant
Go Critical Damping Coefficient = 2*sqrt(Spring Constant/Mass suspended from spring)
Static Deflection given Natural Frequency
Go Static Deflection = (Acceleration due to Gravity)/((2*pi*Frequency)^2)
Gravitational Pull Balanced by Spring Force
Go Weight of Body in Newtons = Stiffness of Constraint*Static Deflection
Restoring Force
Go Force = -Stiffness of Constraint*Displacement of Body
Young's Modulus
Go Young's Modulus = Stress/Strain

16 Rayleigh’s Method Calculators

Maximum Displacement from Mean Position given Velocity at Mean Position
Go Maximum Displacement = (Velocity)/(Cumulative Frequency*cos(Cumulative Frequency*Total Time Taken))
Velocity at Mean Position
Go Velocity = (Cumulative Frequency*Maximum Displacement)*cos(Cumulative Frequency*Total Time Taken)
Maximum Displacement from Mean Position given Displacement of Body from Mean Position
Go Maximum Displacement = Displacement of Body/(sin(Natural Circular Frequency*Total Time Taken))
Displacement of Body from Mean Position
Go Displacement of Body = Maximum Displacement*sin(Natural Circular Frequency*Total Time Taken)
Maximum Displacement from Mean Position given Maximum Kinetic Energy
Go Maximum Displacement = sqrt((2*Maximum Kinetic Energy)/(Load*Natural Circular Frequency^2))
Time Period of Free Longitudinal Vibrations
Go Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)
Natural Circular Frequency given Displacement of Body
Go Frequency = (asin(Displacement of Body/Maximum Displacement))/Time Period
Maximum Displacement from Mean Position given Maximum Potential Energy
Go Maximum Displacement = sqrt((2*Maximum Potential Energy)/Stiffness of Constraint)
Maximum Kinetic Energy at Mean Position
Go Maximum Kinetic Energy = (Load*Cumulative Frequency^2*Maximum Displacement^2)/2
Maximum Potential Energy at Mean Position
Go Maximum Potential Energy = (Stiffness of Constraint*Maximum Displacement^2)/2
Potential Energy given Displacement of Body
Go Potential Energy = (Stiffness of Constraint*(Displacement of Body^2))/2
Natural Circular Frequency given Maximum Velocity at Mean Position
Go Natural Circular Frequency = Maximum Velocity/Maximum Displacement
Maximum Displacement from Mean Position given Maximum Velocity at Mean Position
Go Maximum Displacement = Maximum Velocity/Cumulative Frequency
Maximum Velocity at Mean Position by Rayleigh Method
Go Maximum Velocity = Cumulative Frequency*Maximum Displacement
Time Period given Natural Circular Frequency
Go Time Period = (2*pi)/Natural Circular Frequency
Natural Frequency given Natural Circular Frequency
Go Frequency = Natural Circular Frequency/(2*pi)

Time Period of Free Longitudinal Vibrations Formula

Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint)
tp = 2*pi*sqrt(W/sconstrain)

What is difference between longitudinal and transverse wave?

Transverse waves are always characterized by particle motion being perpendicular to wave motion. A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves.

How to Calculate Time Period of Free Longitudinal Vibrations?

Time Period of Free Longitudinal Vibrations calculator uses Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint) to calculate the Time Period, The Time period of free longitudinal 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 of Free Longitudinal Vibrations using this online calculator? To use this online calculator for Time Period of Free Longitudinal Vibrations, enter Weight of Body in Newtons (W) & Stiffness of Constraint (sconstrain) and hit the calculate button. Here is how the Time Period of Free Longitudinal Vibrations calculation can be explained with given input values -> 4.928936 = 2*pi*sqrt(8/13).

FAQ

What is Time Period of Free Longitudinal Vibrations?
The Time period of free longitudinal 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(W/sconstrain) or Time Period = 2*pi*sqrt(Weight of Body in Newtons/Stiffness of Constraint). Weight of Body in Newtons is the force with which a body is pulled toward the earth & Stiffness of Constraint is the force required to produce unit displacement in the direction of vibration.
How to calculate Time Period of Free Longitudinal Vibrations?
The Time period of free longitudinal 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(Weight of Body in Newtons/Stiffness of Constraint). To calculate Time Period of Free Longitudinal Vibrations, you need Weight of Body in Newtons (W) & Stiffness of Constraint (sconstrain). With our tool, you need to enter the respective value for Weight of Body in Newtons & Stiffness of Constraint 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 Time Period?
In this formula, Time Period uses Weight of Body in Newtons & Stiffness of Constraint. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Time Period = (2*pi)/Natural Circular Frequency
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