A mass M = 0.464 kg moves with an initial speed v = 2.98 m/s on a level frictionless air track. The mass is initially a distance D = 0.250 m away from a spring with k = 844 N/m, which is mounted rigidly at one end of the air track. The mass compresses the spring a maximum distance d, before reversing direction. After bouncing off the spring, the mass travels with the same speed v, but in the opposite direction.

Question

a) Find the total elapsed time until the mass returns to its starting point. (Hint: The mass undergoes a partial cycle of simple harmonic motion while in contact with the spring.)

Answer 1

T=2•π•sqrt(m/k) = 2•π•sqrt(0.464/844)=0.147 s.
The time of “to and fro” motion is T/2 ≈ 0.074 s.
The time of uniform motion before and
after the contact with the spring
t= 2•(D/v) =2•(0.250/2.98)=0.084 s.
The total time is 0.074+ 0.084 =0.158 s.

Answer 2

not the right answer

Answer 3

What is the right answer? I'd like to understand.

Answer 4

no