Question

Two spring-mass systems are pictured. The only difference is that the system on the right has two identical springs side by side (Maybe the effective spring constant is different.).
How does the period of the spring system on the right compare to the period of the system on the left?

• A. The period of the system on the right is twice as long as the period of the system on the left
• B. The period of the system on the right is half as long as the period of the system on the left
• C. The period of the system on the right is longer (but less than twice) the period of the system on the left
• D. The period of the system on the right is less, but greater than half as long as the period of the system on the left
• E. The period of the system on the right is same as the period of the system on the left

Answer 1

The correct option is C The period of the system on the right is longer (but less than twice) the period of the system on the left

The time period of the first (left) system is ,

$T_1=2\pi \sqrt{m/k}=2\pi \sqrt{1/k}$ ................................eq1

The time period of the second (right) system is ,

$T_2=2\pi \sqrt{m/k+k}=2\pi \sqrt{1/2k}$ ...........................eq2 ,

as all the spring are same therefore spring constant $k$ is taken same ,

now dividing eq2 by eq1 ,

$T_2/T_1=1/\sqrt{2}$

or $T_2=\sqrt{2}{T}_1$

option C is correct .