Question

In their discussions of SHM text books sometimes consider a thingy attached to a horizontal spring and moving horizontally on a frictionless surface, instead of the hanging thingy that we have been looking at. Suppose that the two springs and the two thingies are identical. Think about whether these two systems are significantly different in other respects and decide which one of the following statements is true.

• A. The systems have different periods because their motions are aligned differently with the gravitational field.
• B. The hanging system has a slightly smaller period because the weight of the spring has to be accounted for.
• C. The hanging system has a slightly larger period because the weight of the spring has to be accounted for.
• D. The two systems have identical periods, no matter what the weight of the spring is.

Answer 1

The correct option is D The two systems have identical periods, no matter what the weight of the spring is.

The time period of the $0\int$ mass system is given by

$T=2\pi \sqrt{\frac{m}{k}}$

m = mass attached to spring, K = spring constant.

clearly, it is seen that time period only depends on mass attached to spring and spring constant. In the given two cases both are the same no matter what the weight of the spring is.