Question

A mass m is attached to four springs of spring constants 2k, 2k, k, k as shown in figure. The mass is capable of oscillating on a frictionless horizontal floor. If it is displaced slightly and released the frequency of resulting SHM would be –

• A. $\frac { 1 } { 2 \pi }$
• B. $\frac { 1 } { 2 \pi }$ $\sqrt { \left( \frac { 2 \mathrm { k } } { 3 \mathrm {~m} } \right) }$
• C. $\frac { 1 } { 2 \pi }$ $\sqrt { \left( \frac { 3 \mathrm { k } } { \mathrm { m } } \right) }$
• D. $\frac { 1 } { 2 \pi }$ $\sqrt { \left( \frac { 4 \mathrm { k } } { \mathrm { m } } \right) }$

Answer 1

Answer: (C)

$\frac { 1 } { 2 \pi }$ $\sqrt { \left( \frac { 3 \mathrm { k } } { \mathrm { m } } \right) }$

Answer 2

Net force constant k¢ =+ k + k = 3k

T = 2p $\sqrt { \frac { \mathrm { m } } { \mathrm { k } ^ { \prime } } }$