Does Damping Affect the Period of SHM?

In summary, the conversation discusses calculating the period of a damped simple harmonic motion of a spring. The equation for calculating the period is given as T = 2*pi/(W0), where W0 = sqrt(k/m). However, there is a question about whether damping will affect the period. It is mentioned that there is an article discussing this topic on Wikipedia.
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Homework Statement


I've been given (or have calculated) the equation for damped SHM of a spring, and have been told to calculate the period...

I'm given that:

Forced produced by damper: b(dx/dt) where b = 16N/ms
k = 344.5N/m
m = 2kg

Homework Equations



I know that T = 2*pi/(W0)

Where W0 = sqrt(k/m)

But I don't know if damping will have an effect of period? :)

The Attempt at a Solution



Of course, I have tried using the above equation... plug k and m as W0. Would this be correct? Thanks for any help.
 
Physics news on Phys.org

What is damped simple harmonic motion (SHM)?

Damped simple harmonic motion (SHM) is a type of periodic motion in which the restoring force is proportional to the negative of the object's displacement from its equilibrium position and is also opposed by a damping force. This results in the amplitude of the motion decreasing over time.

What is the period of a damped SHM?

The period of a damped SHM is the time it takes for one complete cycle of the motion. It is affected by the damping force and becomes longer as the damping increases.

How do you calculate the period of a damped SHM?

The period of a damped SHM can be calculated using the formula T=2π/ω, where T is the period and ω is the angular frequency. The angular frequency can be calculated using the formula ω=√(k/m-b²/4m²), where k is the spring constant, m is the mass, and b is the damping coefficient.

What is the relationship between damping and period in a damped SHM?

The period of a damped SHM is directly proportional to the damping coefficient. This means that as the damping increases, the period also increases. This is because the damping force decreases the amplitude of the motion, causing the object to take longer to complete one cycle.

What are some real-life examples of damped SHM?

Damped SHM can be observed in many real-life situations, such as a swinging pendulum in air, a car's suspension system, or a vibrating guitar string. In all of these examples, the motion is damped due to the presence of a damping force (air resistance, friction, etc.) and the period of the motion is affected by this damping.

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