For the damped oscillator shown in Figure, the mass of the …

Physics Simple Harmonic Motion (Oscillations) JEE Main / Advanced Problems ( Previous Years) MCQ (Single Correct)

For the damped oscillator shown in Figure, the mass of the block is 200 g, k = 80 Nm –1 and the damping constant b is 40 gs –1 Calculate

The period of oscillation,

Time taken for its amplitude of vibrations to drop to half of its initial value

The time for the mechanical energy to drop to half initial value.

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

[ 0.3 s, 6.93 s, 3.4 s]

As the damping constant, b

(= 0.04 kg s –1 ) <<

the time period T from the equation

is given by,

From the equation x (t) = x m the time T 1/2 for the amplitude to drop to half of its intial value is

or log e

or 0.693 =

or = 6.93 s

E (t) = E (0) ;

;

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