Magnitude of Acceleration of Body in Simple Harmonic Motion Calculator

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Free Vibration of Single DOF Undamped Torsional System

✖Vibrational Amplitude is a measure of its change over a single period.ⓘ Vibrational Amplitude [A']			+10% -10%
✖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%
✖Time in seconds is what a clock reads, it is a scalar quantity.ⓘ Time in seconds [t_sec]			+10% -10%

✖Acceleration is the rate of change in velocity to the change in time.ⓘ Magnitude of Acceleration of Body in Simple Harmonic Motion [a]

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Formula

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Magnitude of Acceleration of Body in Simple Harmonic Motion

Formula

`"a" = "A'"*"ω"^2*sin("ω"*"t"_{"sec"})`

Example

`"0.511062m/s²"="13.2m"*("0.2rad/s")^2*sin("0.2rad/s"*"38s")`

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Magnitude of Acceleration of Body in Simple Harmonic Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds)
a = A'*ω^2*sin(ω*t_sec)
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Acceleration - (Measured in Meter per Square Second) - Acceleration is the rate of change in velocity to the change in time.
Vibrational Amplitude - (Measured in Meter) - Vibrational Amplitude is a measure of its change over a single period.
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.
Time in seconds - (Measured in Second) - Time in seconds is what a clock reads, it is a scalar quantity.

STEP 1: Convert Input(s) to Base Unit

Vibrational Amplitude: 13.2 Meter --> 13.2 Meter No Conversion Required
Angular Velocity: 0.2 Radian per Second --> 0.2 Radian per Second No Conversion Required
Time in seconds: 38 Second --> 38 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = A'*ω^2*sin(ω*t_sec) --> 13.2*0.2^2*sin(0.2*38)

Evaluating ... ...

a = 0.511061586832625

STEP 3: Convert Result to Output's Unit

0.511061586832625 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.511061586832625 ≈ 0.511062 Meter per Square Second <-- Acceleration

(Calculation completed in 00.004 seconds)

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Home » Physics » Mechanical vibrations » Elements of Vibration » Magnitude of Acceleration of Body in Simple Harmonic Motion

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

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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 Formula

Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds)
a = A'*ω^2*sin(ω*t_sec)

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?

Magnitude of Acceleration of Body in Simple Harmonic Motion calculator uses Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds) to calculate the Acceleration, The Magnitude of acceleration of body in simple harmonic motion formula is defined as the product of amplitude, the square of angular velocity, sine of the product of angular velocity, and time. Acceleration is denoted by a symbol.

How to calculate Magnitude of Acceleration of Body in Simple Harmonic Motion using this online calculator? To use this online calculator for Magnitude of Acceleration of Body in Simple Harmonic Motion, enter Vibrational Amplitude (A'), Angular Velocity (ω) & Time in seconds (t_sec) and hit the calculate button. Here is how the Magnitude of Acceleration of Body in Simple Harmonic Motion calculation can be explained with given input values -> 0.511062 = 13.2*0.2^2*sin(0.2*38).

FAQ

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

The Magnitude of acceleration of body in simple harmonic motion formula is defined as the product of amplitude, the square of angular velocity, sine of the product of angular velocity, and time and is represented as a = A'*ω^2*sin(ω*t_sec) or Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds). Vibrational Amplitude is a measure of its change over a single period, 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 & Time in seconds is what a clock reads, it is a scalar quantity.

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

The Magnitude of acceleration of body in simple harmonic motion formula is defined as the product of amplitude, the square of angular velocity, sine of the product of angular velocity, and time is calculated using Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds). To calculate Magnitude of Acceleration of Body in Simple Harmonic Motion, you need Vibrational Amplitude (A'), Angular Velocity (ω) & Time in seconds (t_sec). With our tool, you need to enter the respective value for Vibrational Amplitude, Angular Velocity & Time in seconds 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 Vibrational Amplitude, Angular Velocity & Time in seconds. We can use 1 other way(s) to calculate the same, which is/are as follows -

Acceleration = Angular Velocity^2*Displacement of Body

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