Distance Traveled by Particle in SHM until Velocity becomes Zero Calculator

✖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.ⓘ Velocity [V]			+10% -10%
✖Angular Frequency of a steadily recurring phenomenon expressed in radians per second.ⓘ Angular Frequency [ω]			+10% -10%
✖Displacement is a vector quantity that refers to the change in position of an object from its initial point to its final point.ⓘ Displacement [S]			+10% -10%

✖Maximum Displacement refers to the furthest distance that a particle or object moves away from its equilibrium position during an oscillatory motion.ⓘ Distance Traveled by Particle in SHM until Velocity becomes Zero [S_max]

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Formula

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Distance Traveled by Particle in SHM until Velocity becomes Zero

Formula

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

Example

65.26126 m = \sqrt{\frac{{60 m/s}^{2}}{{10.28508 rev/s}^{2}} + {65 m}^{2}}

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Distance Traveled by Particle in SHM until Velocity becomes Zero Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2)
S_max = sqrt((V^2)/(ω^2)+S^2)
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Maximum Displacement - (Measured in Meter) - Maximum Displacement refers to the furthest distance that a particle or object moves away from its equilibrium position during an oscillatory motion.
Velocity - (Measured in Meter per Second) - 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.
Angular Frequency - (Measured in Hertz) - Angular Frequency of a steadily recurring phenomenon expressed in radians per second.
Displacement - (Measured in Meter) - Displacement is a vector quantity that refers to the change in position of an object from its initial point to its final point.

STEP 1: Convert Input(s) to Base Unit

Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
Angular Frequency: 10.28508 Revolution per Second --> 10.28508 Hertz (Check conversion here)
Displacement: 65 Meter --> 65 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_max = sqrt((V^2)/(ω^2)+S^2) --> sqrt((60^2)/(10.28508^2)+65^2)

Evaluating ... ...

S_max = 65.2612593728107

STEP 3: Convert Result to Output's Unit

65.2612593728107 Meter --> No Conversion Required

FINAL ANSWER

65.2612593728107 ≈ 65.26126 Meter <-- Maximum Displacement

(Calculation completed in 00.020 seconds)

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Indian Institute of Information Technology (IIIT), Guwahati

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< Velocity and Displacement in SHM Calculators

Distance Traveled by Particle in SHM until Velocity becomes Zero

Go Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2)

Velocity of Particle in SHM

Go Velocity = Angular Frequency*sqrt(Maximum Displacement^2-Displacement^2)

Square of Different Distances Traveled in SHM

Go Total Distance Traveled = Maximum Displacement^2-Displacement^2

Distance Traveled in SHM given Angular Frequency

Go Displacement = Acceleration/(-Angular Frequency^2)

Distance Traveled by Particle in SHM until Velocity becomes Zero Formula

Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2)
S_max = sqrt((V^2)/(ω^2)+S^2)

What is Amplitude?

Amplitude refers to the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position during one complete cycle of motion. It is a crucial parameter in describing the intensity or strength of oscillatory or wave-like phenomena.

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

Distance Traveled by Particle in SHM until Velocity becomes Zero calculator uses Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2) to calculate 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 calculate Distance Traveled by Particle in SHM until Velocity becomes Zero using this online calculator? To use this online calculator for Distance Traveled by Particle in SHM until Velocity becomes Zero, enter Velocity (V), Angular Frequency (ω) & Displacement (S) and hit the calculate button. Here is how the Distance Traveled by Particle in SHM until Velocity becomes Zero calculation can be explained with given input values -> 65.26126 = sqrt((60^2)/(10.28508^2)+65^2).

FAQ

What is Distance Traveled by Particle in SHM until Velocity becomes Zero?

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 and is represented as S_max = sqrt((V^2)/(ω^2)+S^2) or Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2). 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, Angular Frequency of a steadily recurring phenomenon expressed in radians per second & Displacement is a vector quantity that refers to the change in position of an object from its initial point to its final point.

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

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 is calculated using Maximum Displacement = sqrt((Velocity^2)/(Angular Frequency^2)+Displacement^2). To calculate Distance Traveled by Particle in SHM until Velocity becomes Zero, you need Velocity (V), Angular Frequency (ω) & Displacement (S). With our tool, you need to enter the respective value for Velocity, Angular Frequency & Displacement and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Maximum Displacement?

In this formula, Maximum Displacement uses Velocity, Angular Frequency & Displacement. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum Displacement = -(Restoring Force/Spring Constant)

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