Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz

In summary, the conversation is about finding the interval in which the amplitude of a damped simple harmonic motion is considered to be zero. The equation for the motion is given as e^-kt cos(2πft) with k=0.7s^-1 and f=3Hz. The question posed is whether the values of t0 and t1, which are the two smallest positive solutions to the equation x(t)=0, make more sense in this context. However, it is clarified that the question is actually about finding when the displacement x(t) is zero, rather than the amplitude.
  • #1
Timburton91
3
0
Homework Statement
Damped Simple Harmonic Motion
Relevant Equations
x(t)=e^-kt cos(2πft)
Hi guys sorry if this is the wrong thread,
I have a damped simple harmonic motion pictured below, i have to find the inerval t=0 and t=1 for which the amplitude of x(t) is considered to be zero.

The behaviour of the graph below can be described as e^-kt cos(2πft)

k=0.7s^-1 and f= 3Hz
IMG_20200315_180120147.jpg
 
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  • #2
I don't really understand the question, what makes more sense to me is to compute the values ##t_0## and ##t_1## that are the two smallest positive solutions to the equation $$x(t)=0$$ is this your question?
 
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  • #3
Not really man, as, i guessed that would be zero.
Gaussian97 said:
I don't really understand the question, what makes more sense to me is to compute the values ##t_0## and ##t_1## that are the two smallest positive solutions to the equation $$x(t)=0$$ is this your question?
 
  • #4
Timburton91 said:
Not really man, as, i guessed that would be zero.
What do you think the question is asking?
 
  • #5
Timburton91 said:
Not really man, as, i guessed that would be zero.
Then, could you please explain to me what is exactly the question? I'm sorry, but I don't understand the question you post in #1.
 
  • #6
The use of "amplitude " in the question may be misleading. In terms of the expression ##e^{-kt}\cos(2\pi ft)##, the amplitude is ##e^{-kt}##. This is never actually zero. I suggest the intended question is to find when the displacement x(t) is zero.
 
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Related to Zero Amplitude Damped Simple Harmonic Motion with k=0.7s^-1 and f=3Hz

1. What is the formula for calculating the period of motion in this scenario?

The formula for calculating the period of motion is T = 2π/ω, where ω is the angular frequency given by ω = √(k/m). In this case, k = 0.7s^-1 and f = 3Hz, so ω = 2πf = 6πs^-1. Therefore, the period of motion is T = 2π/6π = 1/3 seconds.

2. How does the amplitude of the motion change over time?

In zero amplitude damped simple harmonic motion, the amplitude remains constant and does not change over time. This means that the oscillations will continue with the same maximum displacement from equilibrium point.

3. What is the relationship between the frequency and the period of motion?

The frequency and period of motion are inversely proportional. This means that as the frequency increases, the period decreases and vice versa. In this scenario, the frequency is 3Hz and the period is 1/3 seconds.

4. How does the damping coefficient affect the motion?

The damping coefficient, k, affects the motion by determining the rate at which the amplitude of the oscillations decreases. In this scenario, with a k value of 0.7s^-1, the motion is slightly damped, meaning that the amplitude will decrease slowly over time.

5. Can the motion ever reach a state of equilibrium?

In this scenario, the motion will never reach a state of equilibrium because the damping coefficient, k, is not equal to zero. This means that there will always be some amount of damping present, preventing the system from reaching equilibrium.

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