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Position of Particle in SHM Formula

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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. Check FAQs

X = \frac{\sin (ω \cdot t p + θ)}{A}

X - Position of a Particle?ω - Angular Frequency?t_p - Time Period SHM?θ - Phase Angle?A - Amplitude?

Position of Particle in SHM Example

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Here is how the Position of Particle in SHM equation looks like with Values.

Here is how the Position of Particle in SHM equation looks like with Units.

Here is how the Position of Particle in SHM equation looks like.

28.0324 = \frac{\sin (10.2851 \cdot 0.611 + 8)}{0.005}

28.0324 = \frac{\sin (10.2851rev/s \cdot 0.611s + 8°)}{0.005m}

28.0324 = \frac{\sin (10.2851 \cdot 0.611 + 8)}{0.005}

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Position of Particle in SHM Solution

Follow our step by step solution on how to calculate Position of Particle in SHM?

FIRST Step Consider the formula

X = \frac{\sin (ω \cdot t p + θ)}{A}

Next Step Substitute values of Variables

∴

X = \frac{\sin (10.2851rev/s \cdot 0.611s + 8°)}{0.005m}

Next Step Convert Units

∴

X = \frac{\sin (10.2851Hz \cdot 0.611s + 0.1396rad)}{0.005m}

Next Step Prepare to Evaluate

∴

X = \frac{\sin (10.2851 \cdot 0.611 + 0.1396)}{0.005}

Next Step Evaluate

∴

X = 28.0323772372016

LAST Step Rounding Answer

∴

X = 28.0324

Position of Particle in SHM Formula Elements

Variables

Functions

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.

Symbol: X

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Position of a Particle

Angular Frequency

Angular Frequency of a steadily recurring phenomenon expressed in radians per second.

Symbol: ω

Measurement: FrequencyUnit: rev/s

Note: Value should be greater than 0.

Formulas to find Angular Frequency

Time Period SHM

Time Period SHM is time required for the periodic motion.

Symbol: t_p

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period SHM

Phase Angle

Phase Angle is a characteristic of a periodic wave. The angular component periodic wave is known as the phase angle.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Phase Angle

Amplitude

Amplitude is a measure of its change over a single period.

Symbol: A

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Amplitude

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.

Syntax: sin(Angle)

Other formulas in Basic SHM Equations category

Go Time Period of SHM

t p = \frac{2 \cdot π}{ω}

Go Frequency of SHM

f = \frac{1}{t p}

Go Angular Frequency in SHM

ω = \frac{2 \cdot π}{t p}

Go Mass of Particle given Angular Frequency

M = \frac{K}{ω^{2}}

How to Evaluate Position of Particle in SHM?

Position of Particle in SHM evaluator uses Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude to evaluate 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 evaluate Position of Particle in SHM using this online evaluator? To use this online evaluator 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.

FAQs on Position of Particle in SHM

What is the formula to find Position of Particle in SHM?

The formula of Position of Particle in SHM is expressed as Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude. Here is an example- 28.03238 = sin(10.28508*0.611+0.13962634015952)/0.005.

How to calculate Position of Particle in SHM?

With Angular Frequency (ω), Time Period SHM (t_p), Phase Angle (θ) & Amplitude (A) we can find Position of Particle in SHM using the formula - Position of a Particle = sin(Angular Frequency*Time Period SHM+Phase Angle)/Amplitude. This formula also uses Sine function(s).

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Position of Particle in SHM Formula

Position of Particle in SHM Example

Position of Particle in SHM Solution

Position of Particle in SHM Formula Elements

Other formulas in Basic SHM Equations category

How to Evaluate Position of Particle in SHM?

FAQs on Position of Particle in SHM

Variable Name