Position of Particle in SHM 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%
✖Amplitude is a measure of its change over a single period.ⓘ Amplitude [A]			+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 Particle in SHM [X]

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Formula

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Position of Particle in SHM

Formula

`"X" = sin("ω"*"t"_{"p"}+"θ")/"A"`

Example

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

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Position of Particle in SHM Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
Amplitude - (Measured in Meter) - Amplitude is a measure of its change over a single period.

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)
Amplitude: 0.005 Meter --> 0.005 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X = sin(ω*t_p+θ)/A --> sin(10.28508*0.611+0.13962634015952)/0.005

Evaluating ... ...

X = 28.0323772372016

STEP 3: Convert Result to Output's Unit

28.0323772372016 --> No Conversion Required

FINAL ANSWER

28.0323772372016 ≈ 28.03238 <-- Position of a Particle

(Calculation completed in 00.004 seconds)

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Home » Physics » Simple Harmonic Motion(SHM) » Basic Physics » Mechanics » Basic SHM Equations » Position of Particle in SHM

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Created by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

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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

Position of Particle in SHM Formula

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

What is Phase Angle?

The phase angle is the initial offset of the wave or oscillation from a standard reference point. It represents the position within the cycle at t=0

How to Calculate Position of Particle in SHM?

Position of Particle in SHM calculator uses Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude to calculate the Position of a Particle, Position of Particle in SHM formula is defined as a mathematical representation of the location of a particle undergoing simple harmonic motion, determining its displacement from the mean position at any given time, taking into account amplitude, angular frequency, time period, and phase angle. Position of a Particle is denoted by X symbol.

How to calculate Position of Particle in SHM using this online calculator? To use this online calculator for Position of Particle in SHM, enter Angular Frequency (ω), Time Period SHM (t_p), Phase Angle (θ) & Amplitude (A) and hit the calculate button. Here is how the Position of Particle in SHM calculation can be explained with given input values -> 28.03238 = sin(10.28508*0.611+0.13962634015952)/0.005.

FAQ

What is Position of Particle in SHM?

Position of Particle in SHM formula is defined as a mathematical representation of the location of a particle undergoing simple harmonic motion, determining its displacement from the mean position at any given time, taking into account amplitude, angular frequency, time period, and phase angle and is represented as X = sin(ω*t_p+θ)/A or Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude. 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 & Amplitude is a measure of its change over a single period.

How to calculate Position of Particle in SHM?

Position of Particle in SHM formula is defined as a mathematical representation of the location of a particle undergoing simple harmonic motion, determining its displacement from the mean position at any given time, taking into account amplitude, angular frequency, time period, and phase angle is calculated using Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude. To calculate Position of Particle in SHM, you need Angular Frequency (ω), Time Period SHM (t_p), Phase Angle (θ) & Amplitude (A). With our tool, you need to enter the respective value for Angular Frequency, Time Period SHM, Phase Angle & Amplitude 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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