The period of oscillations for a mass suspended from a string depends on the length of the string. It is independent of factors such as mass, acceleration due to gravity, and amplitude of the oscillation.
Step-by-step explanation:
The period of oscillations for a mass suspended from a string undergoing Simple Harmonic Motion (SHM) depends on several factors. However, based on the given options, (e) The period increases with increasing length is the correct statement.
In a simple pendulum, which is a type of oscillating system, the period is determined by the length of the string and the acceleration due to gravity. The period is completely independent of factors such as mass and amplitude of the oscillations. As long as the amplitude is less than about 15°, the period remains nearly constant. Hence, option (a) The period increases with increasing mass is incorrect.
The period of oscillations does not depend on the acceleration due to gravity, so option (b) The period does not depend on acceleration due to gravity is correct.
According to the equations of simple harmonic motion, the period T is proportional to the square root of the length of the string. So, when the length of the string decreases, the period increases. Therefore, option (c) The period increases with decreasing length is incorrect. Similarly, the period is not affected by the amplitude of the oscillation, so option (d) The period increases with increasing amplitude is incorrect.