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Velocity of Particle in SHM Formula

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Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time. Check FAQs

V = ω \cdot \sqrt{{S max}^{2} - S^{2}}

V - Velocity?ω - Angular Frequency?S_max - Maximum Displacement?S - Displacement?

Velocity of Particle in SHM Example

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

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

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

60.03 = 10.2851 \cdot \sqrt{{65.2615}^{2} - 65^{2}}

60.03m/s = 10.2851rev/s \cdot \sqrt{{65.2615m}^{2} - {65m}^{2}}

60.03 = 10.2851 \cdot \sqrt{{65.2615}^{2} - 65^{2}}

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Velocity of Particle in SHM Solution

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

FIRST Step Consider the formula

V = ω \cdot \sqrt{{S max}^{2} - S^{2}}

Next Step Substitute values of Variables

∴

V = 10.2851rev/s \cdot \sqrt{{65.2615m}^{2} - {65m}^{2}}

Next Step Convert Units

∴

V = 10.2851Hz \cdot \sqrt{{65.2615m}^{2} - {65m}^{2}}

Next Step Prepare to Evaluate

∴

V = 10.2851 \cdot \sqrt{{65.2615}^{2} - 65^{2}}

Next Step Evaluate

∴

V = 60.0299800013533m/s

LAST Step Rounding Answer

∴

V = 60.03m/s

Velocity of Particle in SHM Formula Elements

Variables

Functions

Velocity

Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.

Symbol: V

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Velocity

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

Maximum Displacement

Maximum Displacement refers to the furthest distance that a particle or object moves away from its equilibrium position during an oscillatory motion.

Symbol: S_max

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Maximum Displacement

Displacement

Displacement is a vector quantity that refers to the change in position of an object from its initial point to its final point.

Symbol: S

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Displacement

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Velocity and Displacement in SHM category

Go Distance Traveled in SHM given Angular Frequency

S = \frac{a}{- ω^{2}}

Go Distance Traveled by Particle in SHM until Velocity becomes Zero

S max = \sqrt{\frac{V^{2}}{ω^{2}} + S^{2}}

Go Square of Different Distances Traveled in SHM

D total = {S max}^{2} - S^{2}

Go Distance from Start given Restoring Force and Constant K

S max = - (\frac{F restoring}{K})

How to Evaluate Velocity of Particle in SHM?

Velocity of Particle in SHM evaluator uses Velocity = Angular Frequency*sqrt(Maximum Displacement^2-Displacement^2) to evaluate the Velocity, Velocity of Particle in SHM formula is defined as a measure of the speed of a particle undergoing simple harmonic motion, calculated by multiplying the angular frequency by the square root of the difference between the squares of the maximum displacement and the current displacement. Velocity is denoted by V symbol.

How to evaluate Velocity of Particle in SHM using this online evaluator? To use this online evaluator for Velocity of Particle in SHM, enter Angular Frequency (ω), Maximum Displacement (S_max) & Displacement (S) and hit the calculate button.

FAQs on Velocity of Particle in SHM

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

The formula of Velocity of Particle in SHM is expressed as Velocity = Angular Frequency*sqrt(Maximum Displacement^2-Displacement^2). Here is an example- 60.02998 = 10.28508*sqrt(65.26152^2-65^2).

How to calculate Velocity of Particle in SHM?

With Angular Frequency (ω), Maximum Displacement (S_max) & Displacement (S) we can find Velocity of Particle in SHM using the formula - Velocity = Angular Frequency*sqrt(Maximum Displacement^2-Displacement^2). This formula also uses Square Root (sqrt) function(s).

Can the Velocity of Particle in SHM be negative?

No, the Velocity of Particle in SHM, measured in Speed cannot be negative.

Which unit is used to measure Velocity of Particle in SHM?

Velocity of Particle in SHM is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity of Particle in SHM can be measured.

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