Question

Two spring-mass systems are pictured.
The only difference in the systems is the lengths of the springs (and maybe the spring constants). The springs are made of exactly the same stuff and wound exactly the same way.
The spring on the right is simply twice as long (twice as many coils).
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 the same as the period of the system on the left

Answer 1

Answer: (E)

The period of the system on the right is the same as the period of the system on the left

Given : $M_1=M_2=1.0$ kg

As both the springs are made up of same stuff, thus the spring constant of both the springs is same i.e $k_1=k_2$.

Time period of spring-mass system $T=2\pi \sqrt{\frac{M}{k}}$

$⟹$ $T_1=T_2$