A 11.3-kg object oscillates at the end of a vertical spring that has a spring constant of 2.20 ✕ 104 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 N · s/m.(a) Calculate the frequency of the dampened oscillation.
(b) By what percentage does the amplitude of the oscillation decrease in each cycle?

(a) the frequency of the dampened oscillation is 7.02 Hz

(b) percentage decrease in amplitude of the oscillation in each cycle is 2%

Explanation:

Given;

mass of the object = 11.3 kg

the spring constant = 2.2 X 10⁴ N/m.

damping coefficient b = 3.00 N · s/m

Part (a) the frequency of the dampened oscillation

The oscillation frequency is calculated as follows;

The damped frequency

Part (b)  percentage decrease in amplitude of the oscillation in each cycle

The amplitude of the oscillation depends on the damping coefficient (b) and period (T), and it is given as;

After one cycle, the amplitude changes from A(t) to A(t+T), where T is the period of the oscillation.

Percentage decrease in amplitude is gotten by dividing A(t) by A(t+T)

But T = 1/f

Substituting the values of the parameters in the above equation, we will have;

Percentage decrease = 1 - 0.98 = 0.02 = 2%

temp rises, and expansion

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.