Question

A block of mass 200 g executing SHM under the influence of a spring of spring constant k = 90 N m–1 and a damping constant b = 40 g s–1. The time elapsed for its mechanical energy to drop half of its initial value is

• A. 2.5 s
• B. 3.5 s
• C. 4.5 s
• D. 7.5 s

Answer 1

Answer: (B)

3.5 s

Answer 2

The energy of the damped oscillator at any instant t is given by

…… (i)

Where is its initial energy drop to half of its initial value

From eq. (i) we get

Taking natural logarithm on both sides we get

In

….(ii)

Here, In (1/2) $= - 0.693$

Substituting in eq. (ii) we get