Question

A, B, C are identical springs each of spring constant k as shown in Fig. Mass M is displaced slightly along C and released. Find the time period of small oscillation.

• A. T = $2 \pi \sqrt { \frac { m } { k } }$
• B. T = $2 \pi \sqrt { \frac { m } { 2 k } }$
• C. T = $2 \pi \sqrt { \frac { m } { 2 k } }$
• D. T = $2 \pi \sqrt { \frac { 3 m } { 2 k } }$

Answer 1

Answer: (C)

T = $2 \pi \sqrt { \frac { m } { 2 k } }$

Answer 2

Net force as shown in Fig. is

ma = -2kx ora = $\frac { - 2 k } { m }$ x

= $\omega = \sqrt { \frac { 2 k } { m } }$

= $2 \pi \sqrt { \frac { m } { 2 k } }$