Question

Two spring mass systems are pictured. The only differences 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 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 the period of the system on the left.
• E. The period of the system on the right is the same as the period of the system on the left.

Answer 1

Answer: (D)

The period of the system on the right is less, but greater than half the period of the system on the left.

For an object under SHM connected to a spring,

$F=-kx$

where $k$ is the spring constant.

Time period of osciilation=$\frac{2\pi }{\omega }=2\pi \sqrt{\frac{m}{k}}$

The spring constant for system of the right is $k+k=2k$ since to springs are connected in parallel combination.

Hence the time period of system on right is lesser than that on left by a factor of $\frac{1}{\sqrt{2}}$

Hence correct answer is option D.