Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion 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%
✖Vibrational Amplitude is a measure of its change over a single period.ⓘ Vibrational Amplitude [A']			+10% -10%

✖Maximum Acceleration is the rate of change of the velocity of an object with respect to time.ⓘ Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion [a_max]

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Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion

Formula

`"a"_{"max"} = "ω"^2*"A'"`

Example

`"0.528m/s²"=("0.2rad/s")^2*"13.2m"`

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Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude
a_max = ω^2*A'
This formula uses 3 Variables

Variables Used

Maximum Acceleration - (Measured in Meter per Square Second) - Maximum Acceleration is the rate of change of the velocity of an object with respect to 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.
Vibrational Amplitude - (Measured in Meter) - Vibrational Amplitude is a measure of its change over a single period.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity: 0.2 Radian per Second --> 0.2 Radian per Second No Conversion Required
Vibrational Amplitude: 13.2 Meter --> 13.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_max = ω^2*A' --> 0.2^2*13.2

Evaluating ... ...

a_max = 0.528

STEP 3: Convert Result to Output's Unit

0.528 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.528 Meter per Square Second <-- Maximum 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 Maximum Acceleration of Body in Simple Harmonic Motion Formula

Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude
a_max = ω^2*A'

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 Maximum Acceleration of Body in Simple Harmonic Motion?

Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion calculator uses Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude to calculate the Maximum Acceleration, The Magnitude of maximum acceleration of body in simple harmonic motion formula is defined as the product of square of angular velocity and amplitude. Maximum Acceleration is denoted by a_max symbol.

How to calculate Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion using this online calculator? To use this online calculator for Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion, enter Angular Velocity (ω) & Vibrational Amplitude (A') and hit the calculate button. Here is how the Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion calculation can be explained with given input values -> 0.528 = 0.2^2*13.2.

FAQ

What is Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion?

The Magnitude of maximum acceleration of body in simple harmonic motion formula is defined as the product of square of angular velocity and amplitude and is represented as a_max = ω^2*A' or Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude. 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 & Vibrational Amplitude is a measure of its change over a single period.

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

The Magnitude of maximum acceleration of body in simple harmonic motion formula is defined as the product of square of angular velocity and amplitude is calculated using Maximum Acceleration = Angular Velocity^2*Vibrational Amplitude. To calculate Magnitude of Maximum Acceleration of Body in Simple Harmonic Motion, you need Angular Velocity (ω) & Vibrational Amplitude (A'). With our tool, you need to enter the respective value for Angular Velocity & Vibrational Amplitude 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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