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=sin(ωtp+θ)A
X - Position of a Particle?ω - Angular Frequency?tp - Time Period SHM?θ - Phase Angle?A - Amplitude?

Position of Particle in SHM Example

With values
With units
Only example

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.

28.0324Edit=sin(10.2851Edit0.611Edit+8Edit)0.005Edit
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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=sin(ωtp+θ)A
Next Step Substitute values of Variables
X=sin(10.2851rev/s0.611s+8°)0.005m
Next Step Convert Units
X=sin(10.2851Hz0.611s+0.1396rad)0.005m
Next Step Prepare to Evaluate
X=sin(10.28510.611+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.
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.
Time Period SHM
Time Period SHM is time required for the periodic motion.
Symbol: tp
Measurement: TimeUnit: s
Note: Value should be greater than 0.
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.
Amplitude
Amplitude is a measure of its change over a single period.
Symbol: A
Measurement: LengthUnit: m
Note: Value can be positive or negative.
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
tp=2πω
​Go Frequency of SHM
f=1tp
​Go Angular Frequency in SHM
ω=2πtp
​Go Mass of Particle given Angular Frequency
M=Kω2

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 (tp), 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 (tp), 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 (sin) function(s).
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