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An unhappy 0.300-kg rodent, moving on the end of a spring with force constant k = 2.50 N/m, is acted on by a damping force F = -bv. (A) If the constant b has the value 0.900 kg/s, what is the frequency of oscillation of the rodent? (B) For what value of the constant b will the motion be critically damped?

Sagot :

If the rodent oscillates at a frequency of 0.950 kg/s, the motion will be critically dampened at a value of 1.732 kg/s for constant b. to highlight how different from angular frequency ordinary frequency is.

The frequency of an event is its repetitions per unit of time. When contrasting it with spatial frequency, it is also sometimes referred to as temporal frequency.

given damping force: mass = 0.3 kg, k = 2.5 N/m Fx=-bvx+b = 0.950 kg/s

This oscillator is underdamped since the equation of motion for it is mx" + bx' + kx = 0, which results in b2 - 4mk = 0. W = square root(k/m - b2/4m2) yields the angular frequency of oscillation.

For critically damped motion, b2 = 4mk b = 1.732 kg/s, where w = 2.41379 rad/s.

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