Velocity of Particle in SHM Solution

STEP 0: Pre-Calculation Summary
Formula Used
Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2)
v = ω*sqrt(D0^2-D^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
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.
Distance Traveled when Velocity becomes 0 - (Measured in Meter) - Distance Traveled when Velocity becomes 0 is the distance traveled by the particle when the particle loses all its energy and comes to rest after a particular amount of distance is covered.
Distance Traveled - (Measured in Meter) - Distance Traveled defines how much path an object has covered to reach its destination in a given period.
STEP 1: Convert Input(s) to Base Unit
Angular Frequency: 10.28 Revolution per Second --> 10.28 Hertz (Check conversion here)
Distance Traveled when Velocity becomes 0: 70 Meter --> 70 Meter No Conversion Required
Distance Traveled: 65 Meter --> 65 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
v = ω*sqrt(D0^2-D^2) --> 10.28*sqrt(70^2-65^2)
Evaluating ... ...
v = 267.082234527121
STEP 3: Convert Result to Output's Unit
267.082234527121 Meter per Second --> No Conversion Required
FINAL ANSWER
267.082234527121 267.0822 Meter per Second <-- Velocity
(Calculation completed in 00.004 seconds)

Credits

Created by Dipto Mandal
Indian Institute of Information Technology (IIIT), Guwahati
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National Institute Of Technology (NIT), Hamirpur
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10+ Simple Harmonic Motion(SHM) Calculators

Position of Particle in SHM
Go Position of a particle = Amplitude*sin(Angular Frequency*Time Period SHM+Phase Angle)
Distance Traveled by Particle in SHM until Velocity becomes Zero
Go Distance Traveled when Velocity becomes 0 = sqrt((Velocity^2)/(Angular Frequency^2)+Distance Traveled^2)
Velocity of Particle in SHM
Go Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2)
Square of Different Distances Traveled in SHM
Go Total Distance Traveled = Distance Traveled when Velocity becomes 0^2-Distance Traveled^2
Distance Traveled in SHM given Angular Frequency
Go Distance Traveled = Acceleration/(-Angular Frequency^2)
Acceleration in SHM given Angular Frequency
Go Acceleration = -Angular Frequency^2*Distance Traveled
Restoring Force in SHM
Go Restoring Force = Spring Constant*Distance Traveled
Angular Frequency in SHM
Go Angular Frequency = (2*pi)/Time Period SHM
Time Period of SHM
Go Time Period SHM = (2*pi)/Angular Frequency
Frequency of SHM
Go Frequency = 1/Time Period SHM

Velocity of Particle in SHM Formula

Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2)
v = ω*sqrt(D0^2-D^2)

What is SHM?

SHM is defined as a periodic motion of a point along a straight line, such that its acceleration is always toward a fixed point in that line and is proportional to its distance from that point.

How to Calculate Velocity of Particle in SHM?

Velocity of Particle in SHM calculator uses Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2) to calculate the Velocity, The Velocity of Particle in SHM formula is defined as the velocity of the particle executing simple harmonic motion from definition instantaneous velocity. Velocity is denoted by v symbol.

How to calculate Velocity of Particle in SHM using this online calculator? To use this online calculator for Velocity of Particle in SHM, enter Angular Frequency (ω), Distance Traveled when Velocity becomes 0 (D0) & Distance Traveled (D) and hit the calculate button. Here is how the Velocity of Particle in SHM calculation can be explained with given input values -> 267.0822 = 10.28*sqrt(70^2-65^2).

FAQ

What is Velocity of Particle in SHM?
The Velocity of Particle in SHM formula is defined as the velocity of the particle executing simple harmonic motion from definition instantaneous velocity and is represented as v = ω*sqrt(D0^2-D^2) or Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2). Angular Frequency of a steadily recurring phenomenon expressed in radians per second, Distance Traveled when Velocity becomes 0 is the distance traveled by the particle when the particle loses all its energy and comes to rest after a particular amount of distance is covered & Distance Traveled defines how much path an object has covered to reach its destination in a given period.
How to calculate Velocity of Particle in SHM?
The Velocity of Particle in SHM formula is defined as the velocity of the particle executing simple harmonic motion from definition instantaneous velocity is calculated using Velocity = Angular Frequency*sqrt(Distance Traveled when Velocity becomes 0^2-Distance Traveled^2). To calculate Velocity of Particle in SHM, you need Angular Frequency (ω), Distance Traveled when Velocity becomes 0 (D0) & Distance Traveled (D). With our tool, you need to enter the respective value for Angular Frequency, Distance Traveled when Velocity becomes 0 & Distance Traveled and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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