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

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Free Vibration of Single DOF Undamped Torsional System

✖The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity [ω]			+10% -10%
✖Displacement of Body refers to the change in its position or location from an initial point to a final point in a given direction.ⓘ Displacement of Body [d]			+10% -10%

✖Acceleration is the rate of change in velocity to the change in time.ⓘ 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

Formula

`"a" = "ω"^2*"d"`

Example

`"0.5108m/s²"=("0.2rad/s")^2*"12.77m"`

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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 is the rate of change in velocity to the change in time.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Displacement of Body - (Measured in Meter) - Displacement of Body refers to the change in its position or location from an initial point to a final point in a given direction.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity: 0.2 Radian per Second --> 0.2 Radian per Second No Conversion Required
Displacement of Body: 12.77 Meter --> 12.77 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = ω^2*d --> 0.2^2*12.77

Evaluating ... ...

a = 0.5108

STEP 3: Convert Result to Output's Unit

0.5108 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.5108 Meter per Square Second <-- Acceleration

(Calculation completed in 00.004 seconds)

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< 14 Elements of Vibration Calculators

Velocity of Body in Simple Harmonic Motion

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

Magnitude of Acceleration of Body in Simple Harmonic Motion

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

Work Done by Harmonic Force

Go Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference)

Displacement of Body in Simple Harmonic Motion

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

Frequency given Spring Constant and Mass

Go Vibrational Frequency = 1/(2*pi)*sqrt(Spring Stiffness/Mass Attached to Spring)

Angular Frequency

Go Angular Frequency = sqrt(Spring Stiffness/Mass Attached to Spring)

Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion

Go Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude

Maximum Velocity of Body in Simple Harmonic Motion

Go Maximum Velocity = Angular Velocity*Vibrational Amplitude

Magnitude of Acceleration of Body in Simple Harmonic Motion given Displacement

Go Acceleration = Angular Velocity^2*Displacement of Body

Period of Motion in Simple Harmonic Motion

Go Time Period of Oscillations = 2*pi/Angular Velocity

Damping Force

Go Damping Force = Damping Coefficient*Velocity of Body

Inertia Force

Go Inertia Force = Mass Attached to Spring*Acceleration

Spring Force

Go Spring Force = Spring Stiffness*Displacement of Body

Angular Frequency given Time Period of Motion

Go Angular Frequency = 2*pi/Time Period SHM

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

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, The Magnitude of acceleration of body in simple harmonic motion given displacement formula is defined as the square of angular velocity and displacement. 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 -> 0.5108 = 0.2^2*12.77.

FAQ

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

The Magnitude of acceleration of body in simple harmonic motion given displacement formula is defined as the square of angular velocity and displacement and is represented as a = ω^2*d or Acceleration = Angular Velocity^2*Displacement of Body. The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time & Displacement of Body refers to the change in its position or location from an initial point to a final point in a given direction.

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

The Magnitude of acceleration of body in simple harmonic motion given displacement formula is defined as the square of angular velocity and displacement 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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