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*tsec)
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*tsec) --> 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 00.020 seconds)

Credits

Created by Chilvera Bhanu Teja
Institute of Aeronautical Engineering (IARE), Hyderabad
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Verified by Sagar S Kulkarni
Dayananda Sagar College of Engineering (DSCE), Bengaluru
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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*tsec)

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 (tsec) 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*tsec) 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 (tsec). 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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