Q: Will damped oscillations occur for any values of b and k?

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Wave speed is the distance a wave travels in a given period of time. Frequency is the number of oscillations in a given period of time. The third leg of the triangle is wavelength--the distance between peaks of the wave. Given any two of these values for a wave, you can calculate the third.

They can be any values in the domain of the function.

Immediate is a word for occur at any moment.

It can take any value between the maximum and minimum observed values.

trigonometric table gives the values of all the trigonometric functions for any angle. i.e; it gives the numerical values of sine, cosine, tangent etc for any angle between 0 to 180 degrees the values for other angles can be calculated using these.

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Damped oscillation refers to a type of repetitive motion in which the amplitude of the oscillations decreases over time due to the presence of a damping force or mechanism. This damping force absorbs the energy of the system, causing the oscillations to gradually decrease in magnitude until they come to rest.

Damped (or free) oscillation occurs when an object is set to vibrate at its natural frequency while forced oscillation involves the application of a force to keep an object in constant or repetitive motion.

Yes, it is possible to have damped oscillations when a system is at resonance. In such a situation, the amplitude of the oscillations will decrease over time due to the damping factor, even though the frequency of the driving force matches the natural frequency of the system. The presence of damping can affect the sharpness of the resonance peak and the overall behavior of the system at resonance.

A system that is critically damped will return to zero more quickly than an overdamped or underdamped system. Underdamping will result in oscillations for an extended period of time, and while overdamped things will return to zero without much (or any, I think) oscillations they will get there more slowly.

Longitudinal waves, such as sound waves, cannot be polarized because their oscillations occur in the same direction as their propagation. This makes it impossible to filter out any specific orientation of the oscillations.

An example of a transverse wave is light, where the oscillations occur perpendicular to the direction of wave propagation. An example of a longitudinal wave is sound, where the oscillations are in the same direction as the wave propagation, causing compression and rarefaction of the medium.

Wave speed is the distance a wave travels in a given period of time. Frequency is the number of oscillations in a given period of time. The third leg of the triangle is wavelength--the distance between peaks of the wave. Given any two of these values for a wave, you can calculate the third.

Simple harmonic motion is a special type of vibratory motion where an object oscillates back and forth around an equilibrium position with a constant frequency and amplitude. Vibratory motion, on the other hand, is a broader term that includes any motion that involves periodic oscillations or vibrations, not necessarily with a constant frequency or amplitude.

they can occur any where it has to occur with precipitation

They tell you where the graph of the polynomial crosses the x-axis.Now, taking the derivative of the polynomial and setting that answer to zero tells you where the localized maximum and minimum values occur. Two values that have vast applications in almost any profession that uses statistics.

They can be any values in the domain of the function.

Immediate is a word for occur at any moment.