Question

The picture below shows too "snapshots" of the same spring-mass system. In the snapshot on the left, the spring is completely uncompressed and completely unstretched. In the snapshot on the right, the spring is stretched as much as it will be during the oscillating motion.
The time it takes to move from the one position to the other is shown, as is the vertical distance.
With the information in this diagram, what two quantities could be determined?

• A. Spring constant and amplitude of oscillation
• B. Period and amplitude of oscillation
• C. Spring constant and period of oscillation
• D. Spring constant and amount of mass hanging
• E. Amplitude of oscillation and amount of mass hanging

Answer 1

The correct option is B Period and amplitude of oscillation

The left side diagram (unstretched position) shows the mean position of spring. As given, the spring is stretched as much as it will be during motion, therefore $0.080m$ , will be amplitude of oscillation.

Now, spring takes $1.50s$ to reach its extreme position from mean position therefore time period of oscillation will be the time taken by mass to reach again in its initial position (after one oscillation) .i.e. $T=4\times 1.50=6s$ .

And time period, $T=2\pi \sqrt{m/k}$,

Hence, mass and spring constant cannot be calculated by time period.