Position of Particle in SHM Calculator

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✖Amplitude is a measure of its change over a single period.ⓘ Amplitude [A]			+10% -10%
✖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 characteristic of a periodic wave. The angular component periodic wave is known as the phase angle. It is a complex quantity measured by angular units like radians or degrees.ⓘ 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 Particle in SHM [X]

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Formula

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Position of Particle in SHM

Formula

`"X" = "A"*sin("ω"*"t"_{"p"}+"θ")`

Example

`"4.88772"="200m"*sin("10.28rev/s"*"0.6s"+"8°")`

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Position of Particle in SHM Solution

STEP 0: Pre-Calculation Summary

Formula Used

Position of a particle = Amplitude*sin(Angular Frequency*Time Period SHM+Phase Angle)
X = A*sin(ω*t_p+θ)
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.
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 characteristic of a periodic wave. The angular component periodic wave is known as the phase angle. It is a complex quantity measured by angular units like radians or degrees.

STEP 1: Convert Input(s) to Base Unit

Amplitude: 200 Meter --> 200 Meter No Conversion Required
Angular Frequency: 10.28 Revolution per Second --> 10.28 Hertz (Check conversion here)
Time Period SHM: 0.6 Second --> 0.6 Second No Conversion Required
Phase Angle: 8 Degree --> 0.13962634015952 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X = A*sin(ω*t_p+θ) --> 200*sin(10.28*0.6+0.13962634015952)

Evaluating ... ...

X = 4.88771993733902

STEP 3: Convert Result to Output's Unit

4.88771993733902 --> No Conversion Required

FINAL ANSWER

4.88771993733902 ≈ 4.88772 <-- Position of a particle

(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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< 10+ Simple Harmonic Motion(SHM) Calculators

Position of Particle in SHM

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

Distance Traveled by Particle in SHM until Velocity becomes Zero

Go Distance Traveled when Velocity becomes 0 = sqrt((Velocity^2)/(Angular Frequency^2)+Distance Traveled^2)

Velocity of Particle in SHM

Go Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2)

Square of Different Distances Traveled in SHM

Go Total Distance Traveled = Distance Traveled when Velocity becomes 0^2-Distance Traveled^2

Distance Traveled in SHM given Angular Frequency

Go Distance Traveled = Acceleration/(-Angular Frequency^2)

Acceleration in SHM given Angular Frequency

Go Acceleration = -Angular Frequency^2*Distance Traveled

Restoring Force in SHM

Go Restoring Force = Spring Constant*Distance Traveled

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 = Amplitude*sin(Angular Frequency*Time Period SHM+Phase Angle)
X = A*sin(ω*t_p+θ)

What is shm?

Simple harmonic motion 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 Position of Particle in SHM?

Position of Particle in SHM calculator uses Position of a particle = Amplitude*sin(Angular Frequency*Time Period SHM+Phase Angle) to calculate the Position of a particle, The Position of Particle in SHM formula is defined as 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. 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 Amplitude (A), Angular Frequency (ω), Time Period SHM (t_p) & Phase Angle (θ) and hit the calculate button. Here is how the Position of Particle in SHM calculation can be explained with given input values -> 4.88772 = 200*sin(10.28*0.6+0.13962634015952).

FAQ

What is Position of Particle in SHM?

The Position of Particle in SHM formula is defined as 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 X = A*sin(ω*t_p+θ) or Position of a particle = Amplitude*sin(Angular Frequency*Time Period SHM+Phase Angle). Amplitude is a measure of its change over a single period, Angular Frequency of a steadily recurring phenomenon expressed in radians per second, Time Period SHM is time required for the periodic motion & Phase Angle characteristic of a periodic wave. The angular component periodic wave is known as the phase angle. It is a complex quantity measured by angular units like radians or degrees.

How to calculate Position of Particle in SHM?

The Position of Particle in SHM formula is defined as 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 Position of a particle = Amplitude*sin(Angular Frequency*Time Period SHM+Phase Angle). To calculate Position of Particle in SHM, you need Amplitude (A), Angular Frequency (ω), Time Period SHM (t_p) & Phase Angle (θ). With our tool, you need to enter the respective value for Amplitude, Angular Frequency, Time Period SHM & Phase Angle 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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