Work Done by Harmonic Force Solution

STEP 0: Pre-Calculation Summary
Formula Used
Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference)
w = pi*Fh*d*sin(Φ)
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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
Work Done - (Measured in Joule) - Work done by/on a system is energy transferred by/to the system to/from its surroundings.
Harmonic Force - (Measured in Newton) - Harmonic Force refers to a sinusoidal external force of a certain frequency applied to a system.
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.
Phase Difference - (Measured in Radian) - Phase Difference is used to describe the difference in degrees or radians when two or more alternating quantities reach their maximum or zero values.
STEP 1: Convert Input(s) to Base Unit
Harmonic Force: 2.5 Newton --> 2.5 Newton No Conversion Required
Displacement of Body: 12.77 Meter --> 12.77 Meter No Conversion Required
Phase Difference: 1.2 Radian --> 1.2 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
w = pi*Fh*d*sin(Φ) --> pi*2.5*12.77*sin(1.2)
Evaluating ... ...
w = 93.4791821147619
STEP 3: Convert Result to Output's Unit
93.4791821147619 Joule -->0.0934791821147619 Kilojoule (Check conversion here)
FINAL ANSWER
0.0934791821147619 0.093479 Kilojoule <-- Work Done
(Calculation completed in 00.020 seconds)

Credits

Created by Chilvera Bhanu Teja
Institute of Aeronautical Engineering (IARE), Hyderabad
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National Institute of Technology (NIT), Tiruchirapalli
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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

Work Done by Harmonic Force Formula

Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference)
w = pi*Fh*d*sin(Φ)

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 Work Done by Harmonic Force?

Work Done by Harmonic Force calculator uses Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference) to calculate the Work Done, Work Done by Harmonic Force refers to the energy transferred to or from an object or system when subjected to a harmonic force. A harmonic force is a force that varies sinusoidally with respect to displacement. Work Done is denoted by w symbol.

How to calculate Work Done by Harmonic Force using this online calculator? To use this online calculator for Work Done by Harmonic Force, enter Harmonic Force (Fh), Displacement of Body (d) & Phase Difference (Φ) and hit the calculate button. Here is how the Work Done by Harmonic Force calculation can be explained with given input values -> 9.3E-5 = pi*2.5*12.77*sin(1.2).

FAQ

What is Work Done by Harmonic Force?
Work Done by Harmonic Force refers to the energy transferred to or from an object or system when subjected to a harmonic force. A harmonic force is a force that varies sinusoidally with respect to displacement and is represented as w = pi*Fh*d*sin(Φ) or Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference). Harmonic Force refers to a sinusoidal external force of a certain frequency applied to a system, Displacement of Body refers to the change in its position or location from an initial point to a final point in a given direction & Phase Difference is used to describe the difference in degrees or radians when two or more alternating quantities reach their maximum or zero values.
How to calculate Work Done by Harmonic Force?
Work Done by Harmonic Force refers to the energy transferred to or from an object or system when subjected to a harmonic force. A harmonic force is a force that varies sinusoidally with respect to displacement is calculated using Work Done = pi*Harmonic Force*Displacement of Body*sin(Phase Difference). To calculate Work Done by Harmonic Force, you need Harmonic Force (Fh), Displacement of Body (d) & Phase Difference (Φ). With our tool, you need to enter the respective value for Harmonic Force, Displacement of Body & Phase Difference 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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