What is the phase of the simple harmonic motion at t = 10.0 s?

In summary, the function x = (2.0 m) cos[(6π rad/s)t + π/2 rad] describes a simple harmonic motion of a body. At t = 10.0 s, the phase of the motion is 190 rad. The equations V(t) = -12πSin(6πt+(π/2)) and a(t) = -12π(6π)Cos(6πt+(π/2)) can be used to find the velocity and acceleration at t = 10.0 s. There was initially confusion about getting a non-zero answer, but the issue was resolved and the correct answer of zero was obtained.
  • #1
MrAlt
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Homework Statement



The function x = (2.0 m) cos[(6π rad/s)t + π/2 rad] gives the simple harmonic motion of a body. Find the following values at t = 10.0 s.

I am having trouble finding the phase of the motion, The book gives an answer of 190 rad, I am not sure how they got that

Homework Equations



V(t) = -12[itex]\pi[/itex]Sin(6[itex]\pi[/itex]t+([itex]\pi[/itex]/2))
a(t) = -12[itex]\pi[/itex](6[itex]\pi[/itex])Cos(6[itex]\pi[/itex]t+([itex]\pi[/itex]/2))


The Attempt at a Solution



The displacement and acceleration are zero, but for some reason when i plug them into my calculator (it is set to radians) i keep getting answers other than zero, any suggestions?
 
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  • #2
Just found out what i was missing, and feel like a complete fool, sorry to bother you all with this, Thank You
 

Related to What is the phase of the simple harmonic motion at t = 10.0 s?

1. What is the definition of SHM?

SHM, or Simple Harmonic Motion, is a type of periodic motion where the restoring force acting on an object is directly proportional to its displacement from its equilibrium position. It follows a sinusoidal pattern and is characterized by a constant amplitude and frequency.

2. What are the main characteristics of SHM?

The main characteristics of SHM include a constant amplitude, frequency, and period. The motion is also always directed towards the equilibrium position, and the acceleration is directly proportional to the displacement and directed opposite to it.

3. What factors affect the frequency of SHM?

The frequency of SHM is affected by two main factors: the mass of the object and the stiffness of the restoring force. A higher mass or a stiffer restoring force will result in a lower frequency, while a lower mass or a less stiff restoring force will result in a higher frequency.

4. How is SHM related to circular motion?

SHM is closely related to circular motion because both involve a constant acceleration towards a fixed point. In SHM, the acceleration is caused by a restoring force, while in circular motion, it is caused by a centripetal force. Additionally, SHM can be described as a projection of circular motion onto a straight line.

5. What are some real-life examples of SHM?

Some common examples of SHM include the motion of a spring, the motion of a pendulum, and the vibration of a guitar string. Other examples include the motion of a mass attached to a rubber band, the motion of a mass on a horizontal spring, and the motion of a mass on a mass-spring system.

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