Solving SHM: Find Amplitude, Velocity & Time

In summary, the conversation discusses a body with simple harmonic motion (SHM) and its velocity at different distances from the mean position. The amplitude, velocity at the mid-position, and time elapsed between specific instants are requested. The equation x = A sin(ωt) is mentioned as a starting point and it is suggested to write the speed as a function of time. The use of a graph is also suggested.
  • #1
ZackGardner
2
0
A body with SHM has a velocity of 1.3 m/s at a distance of 1.0m from the mean position, and a velocity of 1.0 m/s at a distance of 1.3m from the mean position. Find:

a) The amplitude of the motion.
b) The velocity of the mid-position.
c) The time elapsed between the instants when the body is moving at 1.0 m/s and when it is moving at 1.3 m/s.

Can anyone help me, I have been looking on the internet for formulas but I keep getting websites with different ones & don't know which ones to use. Do I need to draw a graph to answer any part of the question too cheers :)
 
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  • #2
Hints: Start with the equation for position as a function of time:
x = A sin(ωt)

How would you write the speed as a function of time?
 
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Likes Anthony Smith steve

1. What is SHM and how is it related to finding amplitude, velocity, and time?

SHM stands for Simple Harmonic Motion, which is a type of motion where a system oscillates back and forth around an equilibrium point. In order to find the amplitude, velocity, and time of SHM, we need to use equations that describe the motion of the system and solve for these variables.

2. How do you find the amplitude of a system in SHM?

The amplitude of a system in SHM is the maximum displacement from the equilibrium point. To find the amplitude, we can use the equation A = xmax - xeq, where xmax is the maximum displacement and xeq is the equilibrium point.

3. What is the relationship between velocity and time in SHM?

In SHM, velocity and time are inversely proportional. This means that as the time increases, the velocity decreases and vice versa. The equation that describes this relationship is v = -ωAcos(ωt), where ω is the angular frequency and A is the amplitude.

4. How do you calculate the velocity of a system in SHM?

The velocity of a system in SHM can be calculated using the equation v = -ωAsin(ωt), where ω is the angular frequency and A is the amplitude. This equation gives us the instantaneous velocity at any point in time during the SHM.

5. Can you determine the time period of SHM using the given information?

Yes, the time period of SHM can be calculated using the equation T = 2π/ω, where T is the time period and ω is the angular frequency. The angular frequency can be found by using the equation ω = 2πf, where f is the frequency of the system. Once you have found the time period, you can use it to determine the time at which certain events occur during SHM, such as when the system reaches its maximum displacement or velocity.

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