Question

In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS true?

• A. Transmissibility will increase
• B. Transmissibility will decrease
• C. Time period of free oscillations will increase
• D. Time period of free oscillations will decrease

Answer 1

The correct option is C Time period of free oscillations will increase

Additional damper is added in parallel.
Then damping will increase.
But it is still under damped.
But $\xi$ will increase.
Here no unbalanced force is there.


But ${\omega }_d=\sqrt{1-{\xi }^2}.{\omega }_n$ $\left\{{\omega }_n\sqrt{\frac{k}{M}}\right\}$

But as $\xi$ increases

then ${\xi }^2$ will increase

Then ${\omega }_d$ will decrease

Then $T_d=\frac{2\pi }{{\omega }_d}$ will increase