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Distance Traveled by Particle in SHM until Velocity becomes Zero Formula

GoDistance from Start given Restoring Force and Constant K Formula

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

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

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

Distance Traveled by Particle in SHM until Velocity becomes Zero Example

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Here is how the Distance Traveled by Particle in SHM until Velocity becomes Zero equation looks like with Values.

Here is how the Distance Traveled by Particle in SHM until Velocity becomes Zero equation looks like with Units.

Here is how the Distance Traveled by Particle in SHM until Velocity becomes Zero equation looks like.

65.2613 = \sqrt{\frac{60^{2}}{{10.2851}^{2}} + 65^{2}}

65.2613m = \sqrt{\frac{{60m/s}^{2}}{{10.2851rev/s}^{2}} + {65m}^{2}}

65.2613 = \sqrt{\frac{60^{2}}{{10.2851}^{2}} + 65^{2}}

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Distance Traveled by Particle in SHM until Velocity becomes Zero Solution

Follow our step by step solution on how to calculate Distance Traveled by Particle in SHM until Velocity becomes Zero?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S max = \sqrt{\frac{{60m/s}^{2}}{{10.2851rev/s}^{2}} + {65m}^{2}}

Next Step Convert Units

∴

S max = \sqrt{\frac{{60m/s}^{2}}{{10.2851Hz}^{2}} + {65m}^{2}}

Next Step Prepare to Evaluate

∴

S max = \sqrt{\frac{60^{2}}{{10.2851}^{2}} + 65^{2}}

Next Step Evaluate

∴

S max = 65.2612593728107m

LAST Step Rounding Answer

∴

S max = 65.2613m

Distance Traveled by Particle in SHM until Velocity becomes Zero Formula Elements

Variables

Functions

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

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

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 to find Maximum Displacement

Go Distance from Start given Restoring Force and Constant K

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

Other formulas in Velocity and Displacement in SHM category

Go Distance Traveled in SHM given Angular Frequency

S = \frac{a}{- ω^{2}}

Go Velocity of Particle in SHM

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

Go Square of Different Distances Traveled in SHM

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

Go Total Distance Traveled given Velocity and Angular Frequency

D total = \frac{V^{2}}{ω^{2}}

How to Evaluate Distance Traveled by Particle in SHM until Velocity becomes Zero?

Distance Traveled by Particle in SHM until Velocity becomes Zero evaluator uses Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2) to evaluate the Maximum Displacement, Distance Traveled by Particle in SHM until Velocity becomes Zero formula is defined as a measure of the distance covered by a particle in simple harmonic motion from its mean position until its velocity becomes zero, which depends on the velocity, angular frequency, and initial distance of the particle. Maximum Displacement is denoted by S_max symbol.

How to evaluate Distance Traveled by Particle in SHM until Velocity becomes Zero using this online evaluator? To use this online evaluator for Distance Traveled by Particle in SHM until Velocity becomes Zero, enter Velocity (V), Angular Frequency (ω) & Displacement (S) and hit the calculate button.

FAQs on Distance Traveled by Particle in SHM until Velocity becomes Zero

What is the formula to find Distance Traveled by Particle in SHM until Velocity becomes Zero?

The formula of Distance Traveled by Particle in SHM until Velocity becomes Zero is expressed as Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2). Here is an example- 65.26126 = sqrt((60^2)/(10.28508^2)+65^2).

How to calculate Distance Traveled by Particle in SHM until Velocity becomes Zero?

With Velocity (V), Angular Frequency (ω) & Displacement (S) we can find Distance Traveled by Particle in SHM until Velocity becomes Zero using the formula - Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Maximum Displacement?

Here are the different ways to Calculate Maximum Displacement-

Maximum Displacement=-(Restoring Force/Spring Constant)

Can the Distance Traveled by Particle in SHM until Velocity becomes Zero be negative?

Yes, the Distance Traveled by Particle in SHM until Velocity becomes Zero, measured in Length can be negative.

Which unit is used to measure Distance Traveled by Particle in SHM until Velocity becomes Zero?

Distance Traveled by Particle in SHM until Velocity becomes Zero is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Distance Traveled by Particle in SHM until Velocity becomes Zero can be measured.

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