Displacement 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%

✖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 in Simple Harmonic Motion [d]

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Formula

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Displacement of Body in Simple Harmonic Motion

Formula

`"d" = "A'"*sin("ω"*"t"_{"sec"})`

Example

`"12.77654m"="13.2m"*sin("0.2rad/s"*"38s")`

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Displacement of Body in Simple Harmonic Motion Solution

STEP 0: Pre-Calculation Summary

Formula Used

Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds)
d = A'*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

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.
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

d = A'*sin(ω*t_sec) --> 13.2*sin(0.2*38)

Evaluating ... ...

d = 12.7765396708156

STEP 3: Convert Result to Output's Unit

12.7765396708156 Meter --> No Conversion Required

FINAL ANSWER

12.7765396708156 ≈ 12.77654 Meter <-- Displacement of Body

(Calculation completed in 00.004 seconds)

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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

Displacement of Body in Simple Harmonic Motion Formula

Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds)
d = A'*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 Displacement of Body in Simple Harmonic Motion?

Displacement of Body in Simple Harmonic Motion calculator uses Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds) to calculate the Displacement of Body, Displacement of body in simple harmonic motion (SHM) refers to its position relative to its equilibrium position as it oscillates back and forth. The displacement is a key parameter that characterizes the motion of the system. Displacement of Body is denoted by d symbol.

How to calculate Displacement of Body in Simple Harmonic Motion using this online calculator? To use this online calculator for Displacement 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 Displacement of Body in Simple Harmonic Motion calculation can be explained with given input values -> 12.77654 = 13.2*sin(0.2*38).

FAQ

What is Displacement of Body in Simple Harmonic Motion?

Displacement of body in simple harmonic motion (SHM) refers to its position relative to its equilibrium position as it oscillates back and forth. The displacement is a key parameter that characterizes the motion of the system and is represented as d = A'*sin(ω*t_sec) or Displacement of Body = Vibrational Amplitude*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 Displacement of Body in Simple Harmonic Motion?

Displacement of body in simple harmonic motion (SHM) refers to its position relative to its equilibrium position as it oscillates back and forth. The displacement is a key parameter that characterizes the motion of the system is calculated using Displacement of Body = Vibrational Amplitude*sin(Angular Velocity*Time in seconds). To calculate Displacement 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.

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