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Magnitude of Acceleration of Body in Simple Harmonic Motion Formula

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

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Acceleration in mechanical vibrations is the rate of change of velocity of an object with respect to time, describing its oscillatory motion. Check FAQs

a = A' \cdot ω^{2} \cdot \sin (ω \cdot t sec)

a - Acceleration?A' - Vibrational Amplitude?ω - Angular Velocity?t_sec - Time in seconds?

Magnitude of Acceleration of Body in Simple Harmonic Motion Example

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Here is how the Magnitude of Acceleration of Body in Simple Harmonic Motion equation looks like with Values.

Here is how the Magnitude of Acceleration of Body in Simple Harmonic Motion equation looks like with Units.

Here is how the Magnitude of Acceleration of Body in Simple Harmonic Motion equation looks like.

0.5113 = 13.2 \cdot {0.2}^{2} \cdot \sin (0.2 \cdot 38)

0.5113m/s² = 13.2m \cdot {0.2rad/s}^{2} \cdot \sin (0.2rad/s \cdot 38s)

0.5113 = 13.2 \cdot {0.2}^{2} \cdot \sin (0.2 \cdot 38)

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Magnitude of Acceleration of Body in Simple Harmonic Motion Solution

Follow our step by step solution on how to calculate Magnitude of Acceleration of Body in Simple Harmonic Motion?

FIRST Step Consider the formula

a = A' \cdot ω^{2} \cdot \sin (ω \cdot t sec)

Next Step Substitute values of Variables

∴

a = 13.2m \cdot {0.2rad/s}^{2} \cdot \sin (0.2rad/s \cdot 38s)

Next Step Prepare to Evaluate

∴

a = 13.2 \cdot {0.2}^{2} \cdot \sin (0.2 \cdot 38)

Next Step Evaluate

∴

a = 0.51128478042964m/s²

LAST Step Rounding Answer

∴

a = 0.5113m/s²

Magnitude of Acceleration of Body in Simple Harmonic Motion Formula Elements

Variables

Functions

Acceleration

Acceleration in mechanical vibrations is the rate of change of velocity of an object with respect to time, describing its oscillatory motion.

Symbol: a

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Acceleration

Vibrational Amplitude

Vibrational Amplitude is the maximum displacement of an object from its equilibrium position during a mechanical vibration or oscillation.

Symbol: A'

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Vibrational Amplitude

Angular Velocity

Angular Velocity is the rate of change of angular displacement of an object rotating around a fixed axis in mechanical vibrations.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value can be positive or negative.

Formulas to find Angular Velocity

Time in seconds

Time in seconds is the duration of an event or process in mechanical vibrations, typically measured in seconds to analyze vibrational patterns.

Symbol: t_sec

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time in seconds

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.

Syntax: sin(Angle)

Other Formulas to find Acceleration

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

a = ω^{2} \cdot d

Other formulas in Elements of Vibration category

Go Displacement of Body in Simple Harmonic Motion

d = A' \cdot \sin (ω \cdot t sec)

Go Velocity of Body in Simple Harmonic Motion

V = A' \cdot ω \cdot \cos (ω \cdot t sec)

Go Damping Force

F d = c \cdot V

Go Spring Force

P spring = k' \cdot d

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

Magnitude of Acceleration of Body in Simple Harmonic Motion evaluator uses Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds) to evaluate 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 evaluate Magnitude of Acceleration of Body in Simple Harmonic Motion using this online evaluator? To use this online evaluator 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.

FAQs on Magnitude of Acceleration of Body in Simple Harmonic Motion

What is the formula to find Magnitude of Acceleration of Body in Simple Harmonic Motion?

The formula of Magnitude of Acceleration of Body in Simple Harmonic Motion is expressed as Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds). Here is an example- 0.511285 = 13.2*0.200022^2*sin(0.200022*38).

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

With Vibrational Amplitude (A'), Angular Velocity (ω) & Time in seconds (t_sec) we can find Magnitude of Acceleration of Body in Simple Harmonic Motion using the formula - Acceleration = Vibrational Amplitude*Angular Velocity^2*sin(Angular Velocity*Time in seconds). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Acceleration?

Here are the different ways to Calculate Acceleration-

Acceleration=Angular Velocity^2*Displacement of Body

Can the Magnitude of Acceleration of Body in Simple Harmonic Motion be negative?

Yes, the Magnitude of Acceleration of Body in Simple Harmonic Motion, measured in Acceleration can be negative.

Which unit is used to measure Magnitude of Acceleration of Body in Simple Harmonic Motion?

Magnitude of Acceleration of Body in Simple Harmonic Motion is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Magnitude of Acceleration of Body in Simple Harmonic Motion can be measured.

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