An object of unknown mass is hung on the end of an unstretched spring and is released from rest. The acceleration of gravity is 9.81 m/s 2. If the object falls 2.75 cm before first coming to rest, find the period of the motion. Answer in units of s

0.33 s

Explanation:

For this case, as the object is hung on the end of an unstretched spring, we can consider this system as a simple pendulum.

For this system, we can determine the period of the motion using the following formula:

T = 2π√ (L/g)

Where: T = period (in sec), L = lenght of the spring, g = acceleration of garvity = 9.8 m/s²

By the exact time the object is 2.75 cm before coming to rest, that will be the lenght of the spring we can consider (2.75 cm = 0.0275 m)

Finally:

T = 2π√ (0.00275/9.8)

T = 0.33 sec