Velocity of Body in Simple Harmonic Motion Solution

STEP 0: Pre-Calculation Summary
Formula Used
Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds)
V = A'*ω*cos(ω*tsec)
This formula uses 1 Functions, 4 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Velocity of Body - (Measured in Meter per Second) - Velocity of Body refers to the rate at which the position of the body changes with respect to time. It is a vector quantity that describes both the speed and direction of an object's motion.
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
V = A'*ω*cos(ω*tsec) --> 13.2*0.2*cos(0.2*38)
Evaluating ... ...
V = 0.663325984417153
STEP 3: Convert Result to Output's Unit
0.663325984417153 Meter per Second --> No Conversion Required
FINAL ANSWER
0.663325984417153 0.663326 Meter per Second <-- Velocity of Body
(Calculation completed in 00.004 seconds)

Credits

Created by Chilvera Bhanu Teja
Institute of Aeronautical Engineering (IARE), Hyderabad
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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

Velocity of Body in Simple Harmonic Motion Formula

Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds)
V = A'*ω*cos(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 Velocity of Body in Simple Harmonic Motion?

Velocity of Body in Simple Harmonic Motion calculator uses Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds) to calculate the Velocity of Body, The Velocity of body in simple harmonic motion formula is defined as the product of amplitude, angular velocity, cosine of the product of angular velocity, and time. Velocity of Body is denoted by V symbol.

How to calculate Velocity of Body in Simple Harmonic Motion using this online calculator? To use this online calculator for Velocity 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 Velocity of Body in Simple Harmonic Motion calculation can be explained with given input values -> 0.663326 = 13.2*0.2*cos(0.2*38).

FAQ

What is Velocity of Body in Simple Harmonic Motion?
The Velocity of body in simple harmonic motion formula is defined as the product of amplitude, angular velocity, cosine of the product of angular velocity, and time and is represented as V = A'*ω*cos(ω*tsec) or Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(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 Velocity of Body in Simple Harmonic Motion?
The Velocity of body in simple harmonic motion formula is defined as the product of amplitude, angular velocity, cosine of the product of angular velocity, and time is calculated using Velocity of Body = Vibrational Amplitude*Angular Velocity*cos(Angular Velocity*Time in seconds). To calculate Velocity 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.
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