If 2 joules of work is done in raising an apple 8 meters, how much force was exerted?
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Answer:
(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%