Harmonic Motion Homework: Find x(t) from Rest at x=11 cm

In summary, the conversation discussed an object oscillating on a frictionless surface with a frequency of 3.00 Hz and an amplitude of 11.0 cm. The spring constant was found to be 60.75 N/m, and the equation x(t) = 11cos(18.85t) was determined to describe its position as a function of time. A phase constant needed to be added to the equation for it to be accepted by the online homework system.
  • #1
Bob Loblaw
69
0

Homework Statement



A 171 g object on a spring oscillates left to right on a frictionless surface with a frequency of 3.00 Hz and an amplitude of 11.0 cm.
(a) What is the spring constant?
N/m
(b) If the object starts from rest at x = 11.0 cm at t = 0 and the equilibrium point is at x = 0, what equation describes its position (in centimeters) as a function of time (in seconds)?
x(t) =

Homework Equations



(a) was solved and the spring constant was found to be 60.75 N/m

(b) b) x = A cos (omega t)

The Attempt at a Solution



omega is 2pi*3 hZ so omega would be 6pi. Thusly, x(t) = .11 cos (6pi) t
Am I correct? Our online homework system is not accepting my answer and I am not certain if it is because I made a mistake in physics or the syntax of my answer. Could someone verify I am right or wrong?
 
Last edited:
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  • #2
you need to add phase constant to your equation.
 
  • #3
I got it.

I needed to multiply out 6*pi to get its numerical value 18.85 and enclose the argument of the cosine function in parenthesis. 11cos(18.85t) worked.
 

1. What is harmonic motion?

Harmonic motion is a type of periodic motion in which an object's motion follows a repeated pattern over time. It is characterized by the presence of restoring forces that act to bring the object back to its equilibrium position.

2. How is harmonic motion related to springs?

Harmonic motion is commonly observed in systems involving springs, such as a mass attached to a spring. This is because the force exerted by a spring follows Hooke's Law, which states that the force is directly proportional to the displacement from equilibrium. This results in a harmonic motion pattern.

3. How do I find the position of an object in harmonic motion?

In order to find the position of an object in harmonic motion, you need to know the amplitude, frequency, and phase of the motion. These values can be determined from the object's initial position and velocity, as well as any external forces acting on the object.

4. What does x(t) represent in harmonic motion?

x(t) represents the position of the object at a given time t. It is often referred to as the displacement function, as it describes the displacement of the object from its equilibrium position over time.

5. How can I use the given information to find x(t) from rest at x=11 cm?

The given information, specifically the position at rest (x=11 cm), can be used to determine the amplitude of the motion. From there, you can use the equation for harmonic motion, x(t) = A*cos(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle, to find the position of the object at any time t.

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