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Magnitude of Acceleration of Body in Simple Harmonic Motion Calculator

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Elements of Vibration Forced Vibration Free Vibration of Single DOF Undamped Torsional System Undamped Free Vibration

✖Vibrational Amplitude is the maximum displacement of an object from its equilibrium position during a mechanical vibration or oscillation.ⓘ Vibrational Amplitude [A']			+10% -10%
✖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%
✖Time in seconds is the duration of an event or process in mechanical vibrations, typically measured in seconds to analyze vibrational patterns.ⓘ Time in seconds [t_sec]			+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 [a]

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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 in mechanical vibrations is the rate of change of velocity of an object with respect to time, describing its oscillatory motion.
Vibrational Amplitude - (Measured in Meter) - Vibrational Amplitude is the maximum displacement of an object from its equilibrium position during a mechanical vibration or oscillation.
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.
Time in seconds - (Measured in Second) - Time in seconds is the duration of an event or process in mechanical vibrations, typically measured in seconds to analyze vibrational patterns.

STEP 1: Convert Input(s) to Base Unit

Vibrational Amplitude: 13.2 Meter --> 13.2 Meter No Conversion Required
Angular Velocity: 0.200022 Radian per Second --> 0.200022 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*0.200022^2*sin(0.200022*38)

Evaluating ... ...

a = 0.51128478042964

STEP 3: Convert Result to Output's Unit

0.51128478042964 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.51128478042964 ≈ 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 Formula

LaTeX Go

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, Magnitude of Acceleration of Body in Simple Harmonic Motion formula is defined as the maximum rate of change of velocity of an object undergoing simple harmonic motion, which is a type of periodic motion where the object moves back and forth about a fixed point. 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 -> 0.511285 = 13.2*0.200022^2*sin(0.200022*38).

FAQ

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

Magnitude of Acceleration of Body in Simple Harmonic Motion formula is defined as the maximum rate of change of velocity of an object undergoing simple harmonic motion, which is a type of periodic motion where the object moves back and forth about a fixed point 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 the maximum displacement of an object from its equilibrium position during a mechanical vibration or oscillation, Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations & Time in seconds is the duration of an event or process in mechanical vibrations, typically measured in seconds to analyze vibrational patterns.

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

Magnitude of Acceleration of Body in Simple Harmonic Motion formula is defined as the maximum rate of change of velocity of an object undergoing simple harmonic motion, which is a type of periodic motion where the object moves back and forth about a fixed point 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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