What is realy the idea of damped simple harmonic motion?

[efebest]

i am finding damped SHM difficult to understand can anyone give sugestion as to what coul .do

 

[savitri]

Damped functions

Nearly all real world oscillating systems have some dissipatives forces. Therefore, their oscillations die out over time-unless we provide some means for replacing the dissipating mechanism. The decrease in amplitude caused by these frictional forces is called damping-and the corresponding motion is called damped oscillation.

One can view the automobile suspension system as an oscillating system, which if not damped, would keep bobbing up and down for ever, whenever it bumped. The damped function would be an “exponential rate of decay equation x cos (w’t + phi).”

ie Ae^(-(b/m)t) cos (w’t + phi) (1)

Where w = sqrt (k/m – b^2/4m^2) (2)

w’ is the angular frequency.

The exp rate of decay is the amplitude (friction) and decreases with time because of the exponential factor e^(-(b/m)t). Note the negative sign in eq 1.

“b” is the damping factor here. We want to make it large in this case. Look at the b^2 fraction. As b becomes large, eg the shocks pads wear out, the system: cos (sqrt (k/m – b^2/4m^2)t + phi) returns to equilibrium: cos (sqrt (k/m )).

w becomes zero when b becomes large. (k/m – b^2/4m^2)=0
ie b=2sqrt(km)

When eq 2 is in 1, it is called critical damping. The system no longer oscillates when it is disturbed (eg car goes over a bump.) So we want critical damping, or underdamping for best passagenger safety.

If b is greater than 2sqrt(km) = overdamping, no oscill. just a return to equilibrium more slowly.

Hope this is a start.

 

[ravenprp]

The idea of damped simple harmonic motion is that it is a type of motion where an object oscillates back and forth around a central equilibrium point, but with a decreasing amplitude over time due to the presence of a damping force. This damping force can come from various sources, such as friction or air resistance, and it acts to reduce the energy of the oscillating system.

One way to understand damped SHM better is to think of it as a pendulum swinging back and forth. In a perfect scenario, the pendulum would continue to swing with the same amplitude forever. However, in reality, the pendulum will eventually come to a stop due to the presence of air resistance and other factors. This is an example of damped SHM.

To better understand damped SHM, it may be helpful to visualize it using graphs or diagrams. You can also try experimenting with different damping forces and observing how they affect the motion. Another suggestion would be to seek out additional resources, such as online tutorials or textbooks, that provide step-by-step explanations and practice problems.

Overall, the key to understanding damped SHM is to keep practicing and exploring different examples. With patience and persistence, you will eventually grasp the concept and be able to apply it confidently. Don't hesitate to reach out to your teacher or classmates for additional support and clarification.