Question

) A 5kg mass is attached to a spring, and set to oscillate vertically. To get from the top of the oscillation to the bottom takes 0.2s. What is the spring constant of the spring?

4b) If the distance from the top of the oscillation to the bottom is 25cm, what is the maximum speed the mass experiences?

4c) If the mass were doubled, how would that affect the time it takes to get from the top to the bottom?

4d) If the distance from the top to the bottom were doubled, how would this affect the time it takes to get from the top to the bottom? How do you explain this non-intuitive answer?

Answer 1

Moving from top to the bottom will take halftime period of the SHM hence

(a) Now time period can be given as

(b) Amplitude of the oscillation can be given as

then maximum speed will be

(c) As the time period is proportional to the square root of mass hence while doubling the mass, time period become times of initial value hence time in which it takes to move from top to bottom will become

(c) The time period does not depend on the amplitude hence by increasing it, there won't be any change in time. This can be explained in following para.

When the distance/amplitude increases, so the force and corresponding acceleration. Due to this velocity amplitude also get high and hence there is no change in time period.