Question

Find the period of low amplitude vertical vibrations of the system shown The mass of the block is m. The pulley hangs from the ceiling on a spring with a force constant k. The block hangs from an ideal spring.

• A. 2p$\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$
• B. 6p$\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$
• C. 4p$\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$
• D. 8p$\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$

Answer 1

Answer: (C)

4p$\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$

Answer 2

When block is given displacement x spring will stretch by .

\ spring force =

Tension in the string = $\frac { 1 } { 2 }$ × spring force = $\frac { \mathrm { kx } } { 4 }$

T = 2p $\sqrt { \frac { \mathrm { m } } { \frac { \mathrm { k } } { 4 } } }$ = 4p $\sqrt { \frac { \mathrm { m } } { \mathrm { k } } }$