Amplitude given Position Calculator

✖Angular Frequency of a steadily recurring phenomenon expressed in radians per second.ⓘ Angular Frequency [ω]			+10% -10%
✖Time Period SHM is time required for the periodic motion.ⓘ Time Period SHM [t_p]			+10% -10%
✖Phase Angle is a characteristic of a periodic wave. The angular component periodic wave is known as the phase angle.ⓘ Phase Angle [θ]			+10% -10%
✖Position of a Particle is the phase of a vibrating particle at any instant is the state of the vibrating particle regarding its displacement and direction of vibration at that particular instant.ⓘ Position of a Particle [X]			+10% -10%

✖Amplitude is a measure of its change over a single period.ⓘ Amplitude given Position [A]

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Formula

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Amplitude given Position

Formula

`"A" = (sin("ω"*"t"_{"p"}+"θ"))/"X"`

Example

`"0.005m"=(sin("10.28508rev/s"*"0.611s"+"8°"))/"28.03238"`

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Amplitude given Position Solution

STEP 0: Pre-Calculation Summary

Formula Used

Amplitude = (sin(Angular Frequency*Time Period SHM+Phase Angle))/Position of a Particle
A = (sin(ω*t_p+θ))/X
This formula uses 1 Functions, 5 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Amplitude - (Measured in Meter) - Amplitude is a measure of its change over a single period.
Angular Frequency - (Measured in Hertz) - Angular Frequency of a steadily recurring phenomenon expressed in radians per second.
Time Period SHM - (Measured in Second) - Time Period SHM is time required for the periodic motion.
Phase Angle - (Measured in Radian) - Phase Angle is a characteristic of a periodic wave. The angular component periodic wave is known as the phase angle.
Position of a Particle - Position of a Particle is the phase of a vibrating particle at any instant is the state of the vibrating particle regarding its displacement and direction of vibration at that particular instant.

STEP 1: Convert Input(s) to Base Unit

Angular Frequency: 10.28508 Revolution per Second --> 10.28508 Hertz (Check conversion here)
Time Period SHM: 0.611 Second --> 0.611 Second No Conversion Required
Phase Angle: 8 Degree --> 0.13962634015952 Radian (Check conversion here)
Position of a Particle: 28.03238 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (sin(ω*t_p+θ))/X --> (sin(10.28508*0.611+0.13962634015952))/28.03238

Evaluating ... ...

A = 0.00499999950721302

STEP 3: Convert Result to Output's Unit

0.00499999950721302 Meter --> No Conversion Required

FINAL ANSWER

0.00499999950721302 ≈ 0.005 Meter <-- Amplitude

(Calculation completed in 00.004 seconds)

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Created by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

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National Institute Of Technology (NIT), Hamirpur

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< 8 Basic SHM Equations Calculators

Amplitude given Position

Go Amplitude = (sin(Angular Frequency*Time Period SHM+Phase Angle))/Position of a Particle

Position of Particle in SHM

Go Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude

Angular Frequency given Velocity and Distance

Go Angular Frequency = sqrt(Velocity^2/(Maximum Displacement^2-Displacement^2))

Angular Frequency given Constant K and Mass

Go Angular Frequency = sqrt(Spring Constant/Mass)

Mass of Particle given Angular Frequency

Go Mass = Spring Constant/(Angular Frequency^2)

Angular Frequency in SHM

Go Angular Frequency = (2*pi)/Time Period SHM

Time Period of SHM

Go Time Period SHM = (2*pi)/Angular Frequency

Frequency of SHM

Go Frequency = 1/Time Period SHM

Amplitude given Position Formula

Amplitude = (sin(Angular Frequency*Time Period SHM+Phase Angle))/Position of a Particle
A = (sin(ω*t_p+θ))/X

What is SHM?

Simple harmonic motion(SHM) is defined as a periodic motion of a point along a straight line, such that its acceleration is always towards a fixed point in that line and is proportional to its distance from that point.

How to Calculate Amplitude given Position?

Amplitude given Position calculator uses Amplitude = (sin(Angular Frequency*Time Period SHM+Phase Angle))/Position of a Particle to calculate the Amplitude, The Amplitude given Position formula is defined as the phase of a vibrating particle at any instant is the state of the vibrating (or) oscillating particle regarding its displacement and direction of vibration at that particular instant. Amplitude is denoted by A symbol.

How to calculate Amplitude given Position using this online calculator? To use this online calculator for Amplitude given Position, enter Angular Frequency (ω), Time Period SHM (t_p), Phase Angle (θ) & Position of a Particle (X) and hit the calculate button. Here is how the Amplitude given Position calculation can be explained with given input values -> 0.005112 = (sin(10.28508*0.611+0.13962634015952))/28.03238.

FAQ

What is Amplitude given Position?

The Amplitude given Position formula is defined as the phase of a vibrating particle at any instant is the state of the vibrating (or) oscillating particle regarding its displacement and direction of vibration at that particular instant and is represented as A = (sin(ω*t_p+θ))/X or Amplitude = (sin(Angular Frequency*Time Period SHM+Phase Angle))/Position of a Particle. Angular Frequency of a steadily recurring phenomenon expressed in radians per second, Time Period SHM is time required for the periodic motion, Phase Angle is a characteristic of a periodic wave. The angular component periodic wave is known as the phase angle & Position of a Particle is the phase of a vibrating particle at any instant is the state of the vibrating particle regarding its displacement and direction of vibration at that particular instant.

How to calculate Amplitude given Position?

The Amplitude given Position formula is defined as the phase of a vibrating particle at any instant is the state of the vibrating (or) oscillating particle regarding its displacement and direction of vibration at that particular instant is calculated using Amplitude = (sin(Angular Frequency*Time Period SHM+Phase Angle))/Position of a Particle. To calculate Amplitude given Position, you need Angular Frequency (ω), Time Period SHM (t_p), Phase Angle (θ) & Position of a Particle (X). With our tool, you need to enter the respective value for Angular Frequency, Time Period SHM, Phase Angle & Position of a Particle 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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