Question

Four springs & mass is connected as shown in figure. If mass M is displaced horizontally then what is the frequency of S.H.M. ?

• A. $\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm {~K} } { 4 \mathrm { M } } }$
• B. $\frac { 1 } { 2 \pi } \sqrt { \frac { 4 \mathrm {~K} } { \mathrm { M } } }$
• C. $\frac { 1 } { 2 \pi } \sqrt { \frac { \mathrm { K } } { 7 \mathrm { M } } }$
• D. $\frac { 1 } { 2 \pi } \sqrt { \frac { 7 \mathrm {~K} } { \mathrm { M } } }$

Answer 1

Answer: (B)

$\frac { 1 } { 2 \pi } \sqrt { \frac { 4 \mathrm {~K} } { \mathrm { M } } }$

Answer 2

Connected in series so

$\frac { 1 } { \mathrm {~K} _ { \mathrm { eq } } } = \frac { 1 } { 2 \mathrm {~K} } + \frac { 1 } { 2 \mathrm {~K} } = \frac { 1 } { \mathrm {~K} }$

so now

Now all in parallel so

K_eq = K + K + 2K = 4K

& so frequency

f =