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Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement Calculator

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✖Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.ⓘ Angular Velocity [ω]			+10% -10%
✖Displacement of Body is the distance moved by an object from its mean position in a mechanical vibrating system, measured from a reference point.ⓘ Displacement of Body [d]			+10% -10%

✖Acceleration in mechanical vibrations is the rate of change of velocity of an object with respect to time, describing its oscillatory motion.ⓘ Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement [a]

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Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceleration = Angular Velocity^2*Displacement of Body
a = ω^2*d
This formula uses 3 Variables

Variables Used

Acceleration - (Measured in Meter per Square Second) - Acceleration in mechanical vibrations is the rate of change of velocity of an object with respect to time, describing its oscillatory motion.
Angular Velocity - (Measured in Radian per Second) - Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.
Displacement of Body - (Measured in Meter) - Displacement of Body is the distance moved by an object from its mean position in a mechanical vibrating system, measured from a reference point.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity: 0.200022 Radian per Second --> 0.200022 Radian per Second No Conversion Required
Displacement of Body: 12.77931 Meter --> 12.77931 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = ω^2*d --> 0.200022^2*12.77931

Evaluating ... ...

a = 0.511284864113186

STEP 3: Convert Result to Output's Unit

0.511284864113186 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.511284864113186 ≈ 0.511285 Meter per Square Second <-- Acceleration

(Calculation completed in 00.020 seconds)

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< Elements of Vibration Calculators

Velocity of Body in Simple Harmonic Motion

LaTeX Go Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds)

Magnitude of Acceleration of Body in Simple Harmonic Motion

LaTeX Go Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds)

Displacement of Body in Simple Harmonic Motion

LaTeX Go Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds)

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement

LaTeX Go Acceleration = Angular Velocity^2*Displacement of Body

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement Formula

LaTeX Go

Acceleration = Angular Velocity^2*Displacement of Body
a = ω^2*d

What is Simple Harmonic Motion?

Simple harmonic motion is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position.

How to Calculate Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement?

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement calculator uses Acceleration = Angular Velocity^2*Displacement of Body to calculate the Acceleration, Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement formula is defined as a measure of the rate of change of velocity of an object undergoing simple harmonic motion, which is a fundamental concept in mechanical vibrations, describing the acceleration of a body as it oscillates about its equilibrium position. Acceleration is denoted by a symbol.

How to calculate Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement using this online calculator? To use this online calculator for Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement, enter Angular Velocity (ω) & Displacement of Body (d) and hit the calculate button. Here is how the Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement calculation can be explained with given input values -> 0.511285 = 0.200022^2*12.77931.

FAQ

What is Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement?

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement formula is defined as a measure of the rate of change of velocity of an object undergoing simple harmonic motion, which is a fundamental concept in mechanical vibrations, describing the acceleration of a body as it oscillates about its equilibrium position and is represented as a = ω^2*d or Acceleration = Angular Velocity^2*Displacement of Body. Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations & Displacement of Body is the distance moved by an object from its mean position in a mechanical vibrating system, measured from a reference point.

How to calculate Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement?

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement formula is defined as a measure of the rate of change of velocity of an object undergoing simple harmonic motion, which is a fundamental concept in mechanical vibrations, describing the acceleration of a body as it oscillates about its equilibrium position is calculated using Acceleration = Angular Velocity^2*Displacement of Body. To calculate Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement, you need Angular Velocity (ω) & Displacement of Body (d). With our tool, you need to enter the respective value for Angular Velocity & Displacement of Body 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 Acceleration?

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

Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds)

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